NCERT Exemplar Solutions For Grade 8 Mathematics Chapter ...

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NCERT Exemplar Solutions For Grade 8

Mathematics

Chapter 9.- Comparing Quantities

(B) Solved Examples

In examples 1 to 4, there are four options out of which one is correct. Write the

correct answer.

1. A shirt with marked price Rs 800 was sold at Rs 680. The rate of discount on

the shirt is

(a) 10%

(b) 15%

(c) 20%

(d) 10%

Ans: here, we have marked price (M.P) = Rs 800

And Selling price (S.P) = Rs 680

Thus, discount = M.P - S.P

800 680

= Rs 120

Now, Rate of discount Discount

= ×100M.P

120100

800

15 %

Hence, option (b) is the correct answer.


2. If 7

%3

of a number is 42, then the number is

(a) 9800

(b) 8

(c) 1800

(d) 180

Ans: Let required number be .x

Now, according to question,

⇒7

%3

of x = 42

⇒7

3

1

100x = 42

⇒ x = 42 100 3

7

⇒ x = 1800

Hence, option (c) is the correct answer.

3. If the cost price of 10 shirts is equal to the selling price of 8 shirts, then which

of the following is true for the transaction?

(a) Profit of 25%

(b) Loss of 25%

(c) Profit of 20%

(d) Loss of 20%

Ans: here, we have the cost price of 10 shirts is equal to the selling price of 8 shirts.

⇒10 8 CP SP


⇒8

10

CP SP

⇒4

5

CP

SP

Here, SP > CP, thus there will be profit

⇒ Profit % = . .

100 %.

S P C P

C P

=

4. .

5 100 %4

.5

S P S P

S P

=

1

5 100 %4

5

= 1

100 %4

= 25 %

Hence, option (a) is the correct answer.

4. Rs 1600 lent at a compound interest of 5 % per annum, compounded half

yearly for one year will amount to:

(a) Rs 1640

(b) Rs 1680

(c) Rs 1681

(d) Rs 1764

Ans: here, Principle (P) = Rs 1600


⇒ rate of interest (R) = 5

2 % and time (t) = 1 year. So, n = 2

Now, Amount (A) = 1100

n

RP

=

2

51600 1

2 100

=

2

11600 1

40

=

2

411600

40

= 1681

16001600

= Rs 1681

Hence, option (c) is the correct answer.

In examples 5 to 7, fill in the blanks to make the statements true.

5. By selling 50 pens, a shopkeeper lost the amount equal to the selling price of 10

pens. His loss per cent is ………

Ans: let selling price of one pen is .Rs x

So, total selling price (S.P) = Rs 50x

And loss = Rs 10x

Thus, total cost price (C.P) = S.P + loss

= 50x + 10x

= 60x

Now, % loss 100 %loss

CP


10 100 %60

x

x

1 100 %6

50 %3

Hence, by selling 50 pens, a shopkeeper lost the amount equal to the selling price of

10 pens. His loss per cent is 50

%.3

6. The discount per cent is calculated on the ……… price of an article.

Ans: As we know that the discount per cent is calculated on the Marked price of an

article.

7. Amna purchased a toy for Rs 660 including sales tax. If the rate of sales tax is

10 %, then the selling price of the toy is …….

Ans: Let the selling price of the toy be .Rs x

And the rate of sales tax = 10 %

Now, according to question

⇒1

10 660100

x x

⇒ 66010

xx

⇒11

66010

x

⇒ 6010

x

⇒ 600x Rs


Hence, Amna purchased a toy for Rs 660 including sales tax. If the rate of sales tax is

10 %, then the selling price of the toy is Rs 600.

In Examples 8 to 11, state whether the statements are true (T) or false (F).

8. When the interest is compounded half yearly, the number of conversion

periods in a year is four.

Ans:As we know that when the interest is compounded half yearly, the number of

conversion periods in a year is two.

Hence, the given statement is False.

9. Arnav buys a book costing Rs 600. If the rate of sales tax is 7 %, then the total

amount payable by him is Rs 642.

Ans: here, cost price = Rs 600

And sales tax = 1

600 7 42100

Rs

Thus, payable amount = C.P + sales tax

= Rs 600 + Rs 42

= Rs 642

Hence, the given statement is True.

10. After allowing a discount of 15 % on the marked price of an article, it is sold

for Rs 680. The marked price of the article is Rs 800.

Ans:let the marked price of article be Rs .x

Now, according to question

⇒ 15 % 680x of x


⇒1

15 680100

x x

⇒3 68020

xx

⇒17 68020

x

⇒ 4020

x

⇒ 800x Rs


11. Overhead charges, if any, are sometimes included in the cost price.

Ans: As we know that the cost price is the total amount of money that is it costs a

manufacture to produce a given article. It is the original cost of product. It does not

any include any overhead charges.

Hence, the given statement is False.

12. A number is increased by 20% and then it is decreased by 20%. Find the net

increase or decrease percent.

Ans: Let the required number be 100

Now, increase in the number = 20 % of 100 = 1

20 100 20100

So, increased number = 100 + 20 = 120

Decrease in the number = 20 % of 120 = 1

20 120 24100

So, decreased number = 120 24 96

Net decrease = 100 96 4


Thus, net decrease percent = 4

100 % 4 %100

Hence, the net decrease percent is 4.

13.Vishakha offers a discount of 20 % on all the items at her shop and still makes

a profit of 12 %. What is the cost price of an article marked at Rs 280?

Ans: here, we have marked price (M.P) = Rs 280

And discount = 20% of Rs 2801

20 280 56100

Rs

So, selling price (S.P) = Rs 280 56 224Rs

Let the cost price (C.P) be Rs 100.

And profit = 12 % of 100 = 1

12 100 1 2100

Rs

So, selling price (S.P) = Rs 100 12 1 12Rs

Thus, if the selling price is Rs 112, then cost price = Rs 100

If the selling price is Rs 224, cost price = Rs 100

224 200112

Rs

Hence, the required cost price is Rs 200.

14. Find the compound interest on Rs 48,000 for one year at 8 % per annum

when compounded half yearly.

Ans: here, Principal (P) = Rs 48,000

⇒ Rate (R) 8

% 4 %2

and time period (n) = 2

Now, 1100

n

RA P


⇒

2

448,000 1

100A

⇒

2

148,000 1

25A

⇒

2

2648,000

25A

⇒676

48,000625

A

⇒ 51,916.80 A Rs

Thus, compound interest (C.I) A P

51,916.80 48000Rs Rs

3,916.80Rs

Hence, the required compound interest is 3,916.80.Rs

15. Lemons were bought at Rs 60 a dozen and sold at the rate of Rs 40 per 10.

Find the gain or loss percent.

Ans: here, C.P of 1 dozen lemons = Rs 60

.C P of 1 lemon = Rs 60

512

Rs

Thus, C.P of 10 lemons = Rs 50

And S.P of 10 lemons = Rs 40

Here, C.P > S.P, it means there will be loss.

Now, % loss . .

100 %.

C P S P

C P

50 40100 %

50


10100 %

50

20 %

Hence, the required loss percent is 20 %.

Multiple Choice Questions

1. Suppose for the principal P, rate R% and time T, the simple interest is S and

compound interest is C. Consider the possibilities

(i) C>S

(ii) C = S

(iii) C <S Then,

(a) only (i) is correct (b) either (i) or (ii) is correct

(c) either (ii) or (iii) is correct (d) only (iii) is correct

Ans:(a) Let the principal (P) = Rs. 100

Rate of interest (R) = 100% and time period (T) = 2 yr

Then, simple interest =

100

Px R xT =

100 1 0 2

100

x x = Rs20

We know that ,

A = 1 100

T

RP

A = 100 x 11

10 x

11

10 = Rs 121

Compound Interest = A - P = Rs121 - Rs100 = Rs21

so , C > S

Therefore , the correct option is (a).


2. Suppose a certain sum doubles in 2 yr at r% rate of simple interest per annum

and R°/o rate of interest per annum compounded annually. Then,

(a) r < R

(b) R < r

(c)R = r

(d) Cannot be determined

Ans: If the total amount received after 2 yr is the same for both simple interest and

compound interest on the same principal, then the rate of simple interest is greater than

the rate of compound interest.

Hence , R< r

Hence, option (b) is correct.

3. The compound interest on Rs. 50000 at 4% per annum for 2 yr compounded

annually is

(a) Rs. 4000

(b) Rs. 4080

(c) Rs. 4280

(d) Rs. 4050

Ans: Principal (P) = Rs. 50000

Rate of interest (R%) = 4% per annum

Time period (T) = 2 yr

We know that,

A = 1 100

T

RP


=

2

4 50000 1

100

=

2

1 50000 1

25

= 50000×26

25×

26

25 = Rs54080

Compound Interest (CI) = A - P = Rs 54080 - Rs 50000 = Rs 4080

Hence the correct option is (b)

4. If marked price of an article is Rs. 1200 and the discount is 12%, then the

selling price of the article is

(a)Rs. 1056

(b) Rs. 1344

(c) Rs. 1212

(d)Rs.1188

Ans: Marked price of an article = Rs. 1200

Discount % = 12%

Discount selling price = Discount % x marked price

= 12

100x 1200=12 x 12 = Rs.144

Selling price = Marked price – Discount Selling price

= Rs.11200 – Rs. 144

= Rs.1056

Hence the correct option is (a).


5. If 90% of x is 315 km, then the value of x is

(a) 325 km

(b) 350 km

(c) 350 m

Ans: We have, 90% of x = 315 km

90

100 x = 315

x = 315 10

9

x = 350

Hence the correct option is (b)

6.To gain 25% after allowing a discount of 10%, the shopkeeper must mark the

price of the article which cost him Rs. 360 as

(a) Rs. 500

(b) Rs. 450

(c) Rs. 460

(d) Rs. 486

Ans: Let the marked price of the article be Rs. x.

Cost price of the article = Rs. 360

According to the question,

x - x of 10% - 25 360

100

= 360

x -

10

x - 90 = 360


9

10

x = 450

x = 450 10

9

x = 500

So, the Market Price is Rs 500.

Hence the correct option is (a)

7. If a% is the discount percent on marked price x, then discount is

(a) x

a

(b) a

x

(c) ax

100

(d) 100

xa

Ans: We know that discount can be calculated always on marked price, when

discount percentage is given.

Discount = Discount % on marked price = a% of x

Discount =

100

ax

Hence, option (c) is correct.

8. Ashima took a loan of Rs. 100000 at 12% per annum compounded half-yearly.

She paid Rs. 112360. If (1.06)2 is equal to 1.1236, then the period for which she

took the loan is


(a) 2 yr

(b) 1 yr

(c) 6 months

(d) 11

2

Ans: Principal (P) = Rs.100000

Rate of interest (R%) = 12% per annum compounded half-yearly.

Let m be the time period

Amount paid = Rs.112360

We know that,

Amount, when interest is compounded half - yearly

i.e. A =

2

1 200

n

RP

, where n = time period

112360 = 100000

2

12 1

200

m

P

2

53

50

m

= 112360

100000

2

53

50

n

= 2809

2500

2

53

50

=

2

53

50

n

On comparing both sides , we get

2n = 2

n = 1

So the time period is 1yr


Hence option (b) is correct .

9 For calculation of interest compounded half-yearly, keeping the principal the

same, which one of the following is true?

(a) Double the given annual rate and half the given number of years

(b) Double the given annual rate as well as the given number of years

(c) Half the given annual rate as well as the given number of years

(d) Half the given annual rate and double the given number of years

Ans: If interest is compounded half-yearly, then R becomes 2

R and T becomes 2T

and 2T = 2nSo, we have

2

1 200

n

RP

C = A-P

So, half the given annual rate and double the given number of years.

Hence, option (d) is correct.

10. Shyama purchases a scooter costing Rs. 36450 and the rate of sales tax is 9%,

then the total amount paid by her is

(a) Rs. 36490.50

(b) Rs. 39730.50

(c) Rs. 36454.50

(d) Rs. 33169.50

Ans: We know that sales tax is charged on the sale of an item by the government and

is added to the bill amount.

Shyama purchase a scooter of costing = Rs. 36450 Sales tax paid =9%


So, total amount paid by her

= Rs. 36450 of 9% + Rs. 36450

= 9

100× 36450 + 36450

= 9 × 364.5 + 36450 = 3280.5 + 36450 = Rs. 39730.5

Hence, option (b) is correct.

11 The marked price of an article is Rs. 80 and it is sold at Rs. 76, then the

discount rate is

(a) 5%

(b) 95%

(c) 10%

(d) approx 11 %

Ans: The marked price of an article = Rs. 80

Sold price of the article = Rs. 76

We know that,

Selling price = Marked price – Discount Discount

Marked price – Selling price

Discount = Rs.80-Rs.76 = Rs.4

Discount % = 4

80×100 = 5%

Hence, option (a) is correct.

12. A bought a tape recorder for Rs. 8000 and sold it to B. B in turn sold it to C,

each earning a profit of 20%. Which of the following is true?


(a) A and B earn the same profit

(b) A earns more profit than B

(c) A earns less profit than < 5

(d) Cannot be determined

Ans: Cost price of tape recorder for A = Rs.8000

Cost price of tape recorder for B =20% profit on cost price for A

= 20

100× 8000 + 8000

=20 × 80 + 8000

=1600 + 8000

=Rs.9600

Cost price of tape recorder for C=20% profit on cost price for B

= 20

100× 9600 + 9600

=1929 + 9600

=Rs.11520

Here, profit for A= Rs.1600

Profit for B = Rs.1920

So, A earns less profit than B.


13. Latika bought a teapot for Rs. 120 and a set of cups for Rs. 400. She sold

teapots at a profit of 5% and cups at a loss of 5%. The amount received by her is

(a) Rs. 494

(b) Rs.7546


(c) Rs. 506

(d) Rs. 534

Ans:Latika bought a teapot = Rs. 120

Set of cups = Rs. 400

She sold teapot at a profit of 5%,

So, selling price of teapot =5

100 x 120 + 120

= 120

20 +120

= 6 + 120 = Rs.126

Also, she sold cups at a loss of 5%.

So, selling price of cups = 400 –5

100 x 400

= 400 – 20 = Rs. 380

Total amount received by her = Rs. 126 + Rs. 380 = Rs. 506


14. A jacket was sold for Rs. 1120 after allowing a discount of 20%. The marked

price of the jacket is

(a) Rs. 1440

(b) Rs. 1400

(c) Rs. 960

(d) Rs. 866.66

Ans: Let the marked price of the jacket be Rs. x.

Discount % on marked price = 20%


Selling Price of jacket = Rs1120

Then ,

1120 = x - x 20

100

1120 = x - 5

x

4

5

x = 1120

x = Rs1400

So, market price of the jacket is Rs1400

Hence , option (b) is correct .

15. A sum is taken for two years at 16% per annum. If interest is .compounded

after every three months, the number of times for which interest is charged in 2

yrs is

(a) 8

(b)4

(c) 6

(d) 9

Ans: Here since the rate of interest is calculated after every three months. Similarly,

the time period for the amount in a year will be 4 times.

If the amount is taken for 2 yr, it means 4×2 = 8 times charged in 2 yr.

Hence the correct option is (a)

16 The original price of a washing machine which was bought for Rs. 13500

including of 8% VAT, is


(a) Rs. 12420

(b) Rs. 14580

(c) Rs.12500

(d) Rs. 13492

Ans: The price of the washing machine = Rs.13500

VAT [Value Added Tax] is included in the selling price, which is 8%.

The original price of the washing machine including of 8% VAT

= 13500-13500 × 8

100

= 13500-135 × 8 = 13500-1080= Rs.12420

Hence, option (a) is correct.

17. Avinash bought an electric iron for Rs. 900 and sold it at a gain of 10%. He

sold another electric iron at 5% loss which was bought

Rs. 1200. On the transaction, he has a

(a) profit of Rs. 75

(b) loss of Rs. 75

(c) profit of Rs. 30

(d) loss of Rs. 30

Ans: Avinash bought an electric iron = Rs. 900

He sold it, at 10% profit.

So, selling price of the electric iron = 10

100× 900 + 900

= 90+ 900 = Rs. 990

He also sold another electric iron at a 5% loss.


Cost price of another electric iron = Rs.1200

So, selling price of the electric iron = 1200

5

100× 1200

= 1200-60 = Rs.1140

Total amount paid by Avinash for purchasing electric irons = Rs. 900 + Rs.1200 =

Rs.2100

Total received amount = Rs. 990 + Rs. 1140

= Rs. 2130

So, his profit = Rs.2130- Rs.2100 = Rs.30 in transaction.


18 A TV set was bought for t 26250 including 5% VAT. The original price of the

TV set is

(a) Rs. 27562.50

(b) Rs. 25000

(c) Rs. 24937.50

(d) Rs. 26245

Ans:Cost price of TV set = Rs. 26250.

VAT including = 5%

Original price = Cost price of article including VAT = 26250 - 5

100× 26250

= 26250-1312.5

= Rs. 24937.5

So, the original price of the TV set = Rs. 24937.5



19. 40% of [100 – 20% of 300] is equal to

(a) 20

(b) 16

(c) 140

(d) 64

Ans:40% of [100-20% of 300]

40

100 [100 -

20

100300]

40

100[100-60]

40

10040

16


20. Radhika bought a car for Rs. 250000. Next year, its price decreased by 10%

and further next year, it decreased by 12%. In the two years, overall decrease per

cent in the price of the car is

(a) 3.2%

(b) 22%

(c) 20.8%

(d) 8%

Ans: Radhika bought a car for Rs. 250000.


Cost price of a car = Rs.250000

Its price decreased next year by 10%.

So, Price becomes = 250000 - 10

100250000

= 250000 - 25000

= Rs225000

Next year , Price decreases by 12% , price becomes = 225000 - 10

100225000

= 225000 - 27000

=Rs198000

Overall decreased % in two years = 250000 1 980000

250000

100

= 20.8%

Hence the correct option is (c)

Fill in the blanks

21. ……………. is a reduction on the marked price of the article.

Ans:Discount is a reduction on the marked price of the article.

22. Increase of a number from 150 to 162 is equal to an increase of

………………..percent.

Ans:Initial number = 150

Final number = 162

Increased number = 162 -150 = 12


Percent of increased number = 12

150 x 100 = 8%

Therefore , Increase of a number from 150 to 162 is equal to an increase of 8 percent.

23.15% increase in price of an article, which is Rs. 1620, is the increase of

……………..?

Ans:Let the price of the article be Rs. x.

It is given that after 15% increase in price , price became Rs1620

So, x + 15

100 x = 1620

x + 3

20 x = 1620

23

20

x = 1620

x = Rs1408

Increase in price = Rs1620 - Rs1408

= Rs212

Therefore, 15% increase in price of an article, which is Rs. 1620, is the increase Rs212

24.Discount =…………….

Ans:Discount = Market Price (MP) – Selling Price (SP)

Here, MP = Marked price, and SP = Selling price

25.Discount = Discount % of ……………

Ans:Discount = Discount % of marked price


Discount is referred to a reduction given on marked price

26. ………is charged on the sale of an item by the government and is added to the

bill amount.

Ans:Sales tax is charged on the sale of an item by the government and is added to the

bill amount.

Sales tax = Tax % of bill amount

27. Amount when interest is compounded annually, is given by the

formula……………….

Ans: Amount when interest is compounded annually, is given by the formula

A = 1 100

T

RP

where, P = principal, R = rate per- annum and T = time

28. Sales tax = Tax% of……………….

Ans: Sales tax=Tax % of bill amount

29.The time period after which the interest is added each time to form a new

principal, is called the ……………

Ans: The time period after which the interest is added each time to form a new

principal, is called the conversion period.

30.……………… expenses are the additional expenses incurred by a buyer for an

item over and above its cost of purchase.

Ans:Overhead expenses are the additional expenses incurred by a buyer for an item

over and above its cost of purchase.


31.The discount on an item for sale is calculated on the ……………..

Ans:The discount on an item for sale is calculated on the marked price.

32. When principal P is compounded semi-annually at r% per annum for t years,

then amount = ……………..

Ans:When principal P is compounded semi-annually at r% per annum for t years.

i.e Rate = 2

r and Time = 2t

Then , Amount (A) =

2

1 200

t Time

Rate rPrincipal P

A =

2

1 200

t

rP

33.Percentages are to fractions with ………………. equal to 100.

Ans:Percentages are equal to fractions with denominators equal to 100.

34. The marked price of an article when it is sold for 880 after a discount of

12%, is ……………..

Ans:Selling price of an article = Rs.880

Discount % = 12%

We know that, discount is calculated on the marked price.

Let the marked price be Rs. x.

x - 12

100 x = 880

88

100

x = 880


x = Rs1000

Marked Price = Rs1000

Therefore , The marked price of an article when it is sold for 880 after a discount of

12%, is Rs1000.

35. The compound interest on Rs. 8000 for one year at 16% per annum

compounded half-yearly is …………… , given that 21.08 = 1.1664.

Ans:We have,

Principal(P) = Rs.8000

Time period = 1 yr

Rate = 16% per annum compounded half-yearly

A = 1 100

T

RP

A 20.16

(1 )2

P

A = 8000 21.08

A = 8000 21.08

A = 8000 1.1664

A = Rs9331.2

Therefore, The compound interest on Rs. 8000 for one year at 16% per annum

compounded half-yearly is Rs9331.2

36. In the first year on an investment of Rs 6,00,000 the loss is 5% and in the

second year the gain is 10%, the net result is _________.

Ans: Investment amount = Rs6,00,000

Loss in first year = 5%


1st year Investment = 600000 - 5

100600000

= Rs570000

Net Investment when gain is 10% = 570000 +10

100 x 570000= 570000 + 57000

= Rs7627000

37.If amount on the principal of Rs 6,000 is written as 600(35

1 )100

and

compound interest payable half yearly, then rate of interest p.a. is _________ and

time in years is _________.

Ans:Here amount on the principal of 6000 is written as 600( 351 )

100

of and compound interest payable half-yearly, then rate of interest per annum is 10%

and time (in years) is 11

2yr.

38.By selling an article for Rs 1,12,000 a girl gains 40%. The cost price of the

article was _________.

Ans:Selling Price of Article = Rs 1,12,000

Gain% = 40%

Let the cost price of an article be x

x + 40% of x = Selling price of an article

x + 40

100x = 1,12,000

x + 2

5x= 1,12,000


7

5x = 1,12,000

x = Rs 80,000

Therefore , By selling an article for Rs 1,12,000 a girl gains 40%. The cost price of the

article was Rs 80,000

39. The loss per cent on selling 140 geometry boxes at the loss of SP of 10

geometry boxes is equal to ………………..

Ans:Suppose, the selling price of 1 geometry box = 1.

Now, the selling price for 140 geometry boxes = 1 × 140 = Rs. 140

Similarly, selling price of 10 geometry boxes = 1 × 10 = Rs. 10

Loss = selling price of 10 geometry boxes = Rs. 10

So, loss percentage = Loss

CP x 100

By using this formula,

Loss percentage = 62

3%

Hence, The loss per cent on selling 140 geometry boxes at the loss of SP of 10

geometry boxes is equal to 62

3%

40. The cost price of 10 tables is equal to the sale price of 5 tables. The profit per

cent in this transaction is ……………..

Ans:Let the cost price of 1 table be Rs. 1.

The cost price of 10 tables = Sale price of 5 tables Profit

= Cost price of 5 tables

= Rs. 5


Profit percentage = Profit

CP× 100 =

5

5× 100 = 100%

Hence, The cost price of 10 tables is equal to the sale price of 5 tables. The profit per

cent in this transaction is 100%

41.Abida bought 100 pens at the rate of Rs. 3.50 per pen and pays a sales tax of

4%. The total amount paid by Abida is ___________

Ans:Number of pens bought by Abida = 100

Rate of per pen = Rs.3.50 So, cost of 100 pens = 100 x 3.50 = 135

Abida also paid 4% sales tax on Rs. 350.

Hence ,the total amount paid by Abida = 350 x 4

100 + 350 = Rs 364

Therefore, Abida bought 100 pens at the rate of Rs. 3.50 per pen and pays a sales tax

of 4%. The total amount paid by Abidais Rs 364

42. The cost of a tape recorder is Rs. 10800 inclusive of sales tax charged at 8%.

The price of the tape recorder before sales tax was charged, is ……………….

Ans: Suppose the price of the tape recorder before sales tax be Rs. x.

The cost of a tape recorder , inclusive of sales tax charged at 8%. = Rs. 10800

According to the question

x + 8

100× x = 10800

108

100

x = 10800

x = Rs10,000


Hence, The cost of a tape recorder is Rs. 10800 inclusive of sales tax charged at 8%.

The price of the tape recorder before sales tax was charged, is Rs10000

43. 2500 is greater than 500 by …………..%.

Ans:Difference between 2500 and 500 = 2500 – 500 = 2000

Greater % = 500

Difference× 100 =

2000

500×100 = 400%

Hence, 2500 is greater than 500 by 400%

44. Four times a number is a …………….% increase in the number.

Ans:Let the number be x

Four times of x = 4x.

Hence, 4x is greater than x by 4x – x = 3x

Percentage increase in x = 3x

x x 100 = 300%

45. 5% sales tax is charged on an article marked X 200 after allowing a discount

of 5%, then the amount payable is …………….

Ans:Given marked price of the article = 1200 Discount = 5%

Selling price = 200 – 5

100× 200 =200 -10 = Rs.190

Selling price (including 5% sales tax) = 190 + 5

100× 190= 190+ 9.5 = Rs.199.5

Amount to be paid = Rs. 199.50


Therefore, 5% sales tax is charged on an article marked X 200 after allowing a

discount of 5%, then the amount payable is Rs. 199.50

State whether the statements are true (T) or false (F).

46. To calculate the growth of bacteria if the rate of growth is known, the formula

for calculation of amount in compound interest can be used.

Ans:For calculating the growth of a bacteria for the rate of growth is known, then

formula for calculation of amount in compound interest.where, A = growth after n

years, P = initial number of bacteria and R = rate of growth can be used .

Hence the given statement is true.

47.Additional expenses made after buying an article are included in the cost price

and are known as Value Added Tax.

Ans: The given statement is false. VAT is always included in the selling price.

Therefore, Value Added Tax is always added to the selling price.

48.Discount is a reduction given on the cost price of an article.

Ans: Discount is termed as the reduction given on market price of an article , so the

statement is False .

49. Compound interest is the interest calculated on the previous year’s amount.

Ans:Compound interest is referred to as the interest calculated on the previous year’s

amount.

Hence the given statement is true.

50.C.P. = M.P. – Discount.


Ans:The given statement is False as

Selling price = Market price – discount

51. A man purchased a bicycle for Rs 1,040 and sold it for Rs 800. His gain

percent is 30%.

Ans:Given, CP of a bicycle = Rs. 1,040

SP of this bicycle = Rs. 800

We know that, loss = cost price – selling price = 1040 = 800 = Rs. 240

Now we know that ,

Loss% = Loss

CP× 100 =

240

1040× 100 = 23.07%

Hence, the given statement is false.

52. Three times a number is a 200% increase in the number, then one-third of the

same number is a 200% decrease in the number.

Ans: Let us suppose x be the number.

So, three times of x is given by 3x

Difference = 3x-x = 2x

Percentage increase in x = 2x

x x 100 = 200%

One third of x is given by 3

x

Difference = x - 3

x

= 2

3

x


Decreased % is given by =2

3

xx

100

= 2

3×100

= 66.66%

53. Simple interest on a given amount is always less than or equal to the

compound interest on the same amount for the same time period and at the same

rate of interest per annum.

Ans:The S.I. and C.I. For some amount the equal rate of interest is always equal for

the first year.

The S.I. is less than the C.I. for an equal amount on the same rate of interest for the

second year.

Hence,the given statement is false.

54.The cost of a sewing machine is Rs. 7000. Its value depreciates at 8% per

annum. Then, the value of the machine after 2 yr is Rs. 5924.80.

Ans:Given, Principal = Rs.7000

Depreciation Rate = 3% per annum

Time period = 2 yr

According to the Question ,

A = 1 100

n

RP

A =

2

8 7000 1

100

A = 23 23

700025 25


A = Rs5924.80

Hence the given statement is True.

55. If the discount of Rs. y is available on the marked price of Rs. x, then the

discount percent is x

y x 100%.

Ans:Given,

Marked Price = Rs x

Discount available = Rs y

Discount% =

Discount

Marked Price x 100 =

y

x x 100%

Hence the given statement is False .

56. Number of students appearing for class X CBSE examination increases from

91422 in 1999-2000 to 116054 in 2008-09. Increase in the number of students

appeared is approximately 27%.

Ans:Increase in students from 2008-09 to 1999-2000

= 116054 – 91422 = 24632

%Increase in students =

noof studentsincrease

noof studentsin previous year× 100

=24632

91422×100

= 27%(approx)

Hence the given statement is True..


57. Selling price of 9 articles is equals to the cost price of 15 articles .In this

transaction the profit of 662

3%

Ans:SP of 9 articles =CP of 15 articles

Here in transaction, cost price of 6 articles is the profit

Profit% = 6

9×100 =

200

3 =

2 66

3%


58.The compound interest on a sum of Rs. P for T years at R% per annum

compounded annually is given by the formula, 1 100

RP

Ans:The Formula for compound interest on a sum of Rs. P for T years at

R% per annum compounded annually is given by 1 100

T

RP

Hence the given statement is False .

59.In the case of gain, SP= 100

100

gain

Ans:The statement given is true.

We know that,

Gain is given by = Selling price - Cost price

Therefore now gain % =

100

Gain

Cost price


Therefore Selling price = 100 %

100100

Gain

It should be noted that gain or the loss is always calculated based on the cost price.

60.In the case of loss, CP= 100

100

SP

Loss

Ans:The statement is false.

Loss is given by = Cost price - Selling price.

Therefore Loss % =

100

Loss

Cost price

Therefore , Cost price = 100

100 %

Selling priceLoss

61.The value of a car, bought for Rs. 440000 depreciates each year by 10% of its

value at the beginning of that year. So, its value becomes Rs. 308000 after three

years.

Ans:The above statement if false,

The value of the car which is the principal= Rupees 440000 Rate of depreciation (R%)

=10% per annum Time period (T) = 3 yr

The value of the car after depreciation in 3 years is given by

A= P 1100

T

R

= 440000

3

101

100

= 440 729 320760Rupees

62. The cost of a book marked at Rs. 190 after paying a sales tax of 2% is Rs. 192.


Ans:The statement given is false.

The marked price of the book = Rs.190

Sales tax = 2%

The cost price of the book after 2% sales tax = 190 + 2

19010

= 190+38 = rupees 193.8

63.The buying price of 5 kg of flour with the rate Rs. 20 per kg, when 5% sales

tax is added on the purchase, is Rs. 21.

Ans: The above statement is true.

The total flour bought = 5 kg

Rate of one kg flour = 5 kg

The cost of 5 kg flour with 5% sales tax = 5 5

20 5 2010

= 100 5

10010

= 105 rupees.

The per kg flour rate after 5% sales tax = 105

5= Rupees 21

64.The original price of a shampoo bottle bought for Rs. 324, if 8% VAT is

included in the price, is Rs. 300.

Ans:The above statement is false.

The original price of a shampoo bottle = rupees 300

The cost price of the shampoo bottle after 8% VAT

= 300+ 8

300100


= 300 + 24 = Rupees 324.

65. Sales tax is always calculated on the cost price of an item and is added to the

value of the bill.

Ans:The above statement of false as the sales tax is always calculated on the selling

price of an item and is added to the value of the bill.

66. In a factory, women are 35% of all the workers, the rest of the workers being

men. The number of men exceeds that of women by 252. Find the total number of

workers in the factory.

Ans:

It is given that the percentage of women in the factory = 35%

The percentage of men in the factory = 100 -35 = 65%

Let the number of the persons in the factory be x.

Based on the question,

65 35 252

100 100x x

65 35252

100

x x

30 100

x =252

x = 2520

3 = 840

So there fore the total numberof workers in the factory.


67.Three bags contain 64.2 kg of sugar. The second bag contains 4

5 of the

contents of the first and the third contains 45 ½ % of what there is in the second

bag. How much sugar is there in each bag?

Ans:From the question we can say that the total weight of sugar in three bags = 64.2

kg.

Now let us assume that the first bag contains x kg sugar.

The secondbag contains = x 4

5=

4

5

x kg

The third bag contains = 4 91% 91 5 2 250

xx kg

As per the question,

4 91% 5 2

x 64.2

541x = 64.2 250

x = 16050

541= 29.67 kg

So now the first bag contains the sugar = 29.67 4

23.73 . 5

kg and

The third bag contains the sugar = 91

29.67 10.8 . 250

kg

68. Find the SP, if

(a) MP = Rs. 5450 and discount = 5%

(b) MP = Rs.1300 and discount = 15%

Ans:

(a) Here from the question Marked price = 5450 and the discount percentage is = 5%


Therefore the selling price = Marked price - %

100

DiscountMarked price

= 1300 -15

1300 1300 19.5 1 280.5100

Rupees

69. Find the MP, if

(a) SP = Rs. 495 and discount = 1%

(b) SP = Rs. 9250 and discount = 7 ½ %

Ans: (a) Selling price (SP) = 7495 and discount % = 1%

Now let the marked price be rupees x

Therefore selling price = Marked price - %

100

DiscountMP

495 = x - 1

100x , on solving we get

x = 500

Hence the marked price = Rupees 500.

(b) SP = Rs. 9250 and discount = 7 ½ %

The selling price (SP) = Rupees 9250

Discount % = 7 ½ % = 15

%2

Let the marked price be rupees x.

Therefore the selling price = Marked price - %

100

DiscountMP

9250 = x - 15

2 100x


9250 = 185

200

x

1 0000x rupees

Hence the marked price = rupees 10000

70. Find discount in percent when

(a) MP = Rs.625 and SP = Rs.562.50

(b) MP = Rs.900 and SP = Rs.873

Ans:

(a) MP = Rs.625 and SP = Rs.562.50

Since discount = marked price - selling price = 625-562.5 = rupees 62.5

Therefore discount % = 62.5

100 100 1 0% 625

Discount

Marked price

(b) MP = Rs.900 and SP = Rs.873

The mark price (MP) = Rupees 900

Selling price (SP) = 873

Therefore discount = marked price -selling price = 900-873= Rupees 27

Therefore discount % = 27

100 100 3% 900

Discount

Marked price

71. The marked price of an article is Rs. 500. The shopkeeper gives a discount of

5% and still makes a profit of 25%. Find the cost price of the article.

Ans: It is given that the marked price of an article = Rs.500 Discount % = 5%

It is given that the profit made by the owner = 25%

So now let the cost price of the article be Rs. x


The cost price after 5% discount = 500 - 5

500100

= 500 - 25 = Rupees 475.

As per the question,

(100+25)% of x = 475

So now after solving, x = Rupees 380.

Hence the cost price of the article is Rupees 380.

72. In 2007-08, the number of students who appeared for Class X examination

was 105332 and in 2008-09 the number was 116054. If 88151 students pass the

examination in 2007-08 and 103804 students in 2008-09. What is the increase or

decrease in pass percentage in class X result?

Ans: From the question the number of students who appeared in 2007-08 = 105332

Number of students appeared in 2008-09 = 116054

The number of students passed in 2007-08 = 88151

The number of students passed in 2008-09 = 103804

The pass percentage of students for the period of 2007-08

= 2007 08

100 2008 09

Number of students passed in

Number of studentsappeared in

= 88151

100105332

= 83.68%

The passed percentage of students in 2008-09

= 2008 09

100 2008 09

Number of students passed in

Number of studentsappeared in


= 103804

1001 16054

= 89.44%

There fore the total increase in percentage would be = 89.44 - 83.68 = 5.76%

73.A watch worth Rs. 5400 x is offered for sale at Rs. 4500. What per cent

discount is offered during the sale?

Ans:The marked price of the watch = Rs.5400

The selling price = Rs.4500

Discount = Marked price – Selling price = Rs.5400 – Rs.4500 = Rs.900

Therefore discount % =

100

Discount

marked price

= 900

54

= 150

9=

50%

3

74. In the year 2001, the number of malaria patients admitted in the hospitals of a

state was 4375. Every year this number decreases by 8%. Find the number of-

patients in 2003.

Solution. The number of malaria patients admitted in a hospital in 2001 = 4375

Rate of decrement of malaria patients = 8%

Time period = 2 yri.e.2003-2001=2 yr

Let the number of patients in 2003 be A.

Ans: From the question we can say that the number of malaria pateints which were

admitted in a hospital in 2001 = 4375

The rate of decrement of malaria patients = 8%

Time period = 2 year which is between 2003 -2001

Let the number of patients in 2003 be A.


Let us use the formula,

A = P 1100

T

R

= 4375

2

81

100

= 4375

2

23

25

= 3703

Therefore the number of patients in 2003 was 3703.

75. Jyotsana bought a product for Rs. 3155 including 4.5% sales tax. Find the

price before tax was added.

Ans: From the question we can say that the product bought by Jyotsana for Rs. 3155

including 4.5% sales tax.

Let the price of the product before sales tax be Rs. x .

So now, 4.5

100x x =3155

On solving we get .3019.14x Rs

76. An average Urban Indian uses about 150 L of water everyday.

Activity Litres per person per day

Drinking 3

Cooking 4

Bathing 20


Sanitation 40

Washing clothes 40

Washing utensils 20

Gardening 23

Total 150

(a) What per cent of water is used for bathing and sanitation together per day?

Ans: From the given details, water used for bathing per day = 20 L

Water used for sanitation = 40 L

Total water used per day = 150 L

The percentage of water that is used for bathing and sanitation together per day

= 20 40 60

100 100150 150

= 600

40% 15

(b) How much less per cent of water is used for cooking in comparison to that

used for bathing?

Ans: Water which is been used to cook per day = 4L

Water which is been used for bathing per day = 20L

The total difference between the water used for cooking and bathing = 20-4 = 16 L

Therefore 16L of water is less used for cooking in comparison of bathing.

In percentage = 16

100150

= 32

3%.


(c) What per cent of water- is used fdr drinking, cooking and gardening

together?

Ans: The water which is been used for drinking per day = 3L

Water used for cooking per day = 4L

Water used for gardening per day = 23L

Total water which is been used for drinking , cooking and gardening = 3+4+23 = 30L.

In percentage the value is = 30

100 20%.150

77. In 1975, the consumption of water for human use was about 3850 cu km/yr. It

increased to about 6000 cu km/yr in the year 2000.

Find the per cent increase in the consumption of water from 1975 to 2000. Also,

find the annual per cent increase in consumption

(assuming water consumption increases uniformly).

Ans: The consumption of water for human in 1975 = 3850 cu km/yr

The consumption of water for human in 2000 = 6000 cu km/yr

Increase in consumption of water in 1975 to 2000 = 6000 - 3850 =2150 cu km/yr

In percentage = 2150

100 55.84% 3850

In 25 years total increase in water consumption = 2150 cu km/yr

Therefore per year annual consumption = 2150

50= 86 cu km/yr

Therefore now, consumption in percentage is given by = 86

1003850

= 8600

3850 =2.23%

78. Harshna gave her car for service at service station on 27-05-2009 and was

charged as follows


(a) 3.10 L engine oil @ Rs. 178.75 per litre and VAT @ 20%.

(b) Rs. 1105.12 for all other services and VAT @ 12.5%.

(c) Rs. 2095.80 as labour charges and service tax @ 10%.

(d) 3% cess on service tax.

Find the bill amount.

Ans:

(a) The total litres of engine oil used = 3.10L

Rate of engine oil per litres =Rs. 178.75

The cost of engine oil = 3.10 x 17875= Rs. 554.125

The cost of engine oil including 20% VAT = 554.125 + 554.125 20

100

= 554.125 + 554.125

5

= Rs. 664.95

(b) Amount paid for all the services = Rs. 1105.12

Amount paid including 12.5% VAT = 1105.12 + 12.5

1105.12 100

= Rs.1243.26

(c) Labour charges = Rs. 2095.90

Service tax = 10%

The total labour charges including 10% service tax

= 2095.80+ 10

2095.8 2095.80 209.58 . 2305.38100

Rs

(d) Cess on service tax at 3% = 209.583

2.095 3100


= Rs. 6.29

Thus the total bill amount = Rs. 664.95+ Rs.1243.26+ Rs.2305.38+Rs.6.29 = Rs.

4219.88

79. Given, the principal = Rs.40000, rate of interest = 8% per annum

compounded annually. Find

(a) Interest if the period is one year.

(b) Principal for the 2nd year.

(c) Interest for 2nd year.

(d) Amount if the period is two year.

Ans: Given, principal (P)= Rs.40000

Rate of interest (R) = 8% per annum

a) Compound interest for one year,

1100

n

RA P

1

840000 1

100

[ ∵ n = 1 year]

10840000

100

So, 400 108 .43200A Rs

Compound Interest, 43200 40000 .3200CI A P Rs

b) Amount of first year = Principal of second year = Rs. 43200

c) Now, For second year,

Principal = Rs. 43200

Rate of interest, R = 8% per annum


Time, n = 1 year

1100

n

RA P

1

843200 1

100

[ ∵ n = 1 year]

10843200

100

So, 432 108 .46656A Rs

Compound Interest, 46656 43200 .3456CI A P Rs

d) For period of 2 years, Amount is A= .46656Rs

80. In Delhi University, in the year 2009-10, 49000 seats were available for

admission to various courses at graduation level. Out of these 28200 seats were

for the students of General Category while 7400 seats were reserved for SC and

3700 seats for ST. Find the percentage of seats available for

(a) students of General Category.

(b) students of SC Category and ST Category taken together.

Ans: The total number of seats which are available for admission in 2009-10 = 49000

Seats reserved for General Category students = 28200

Seats reserved for SC Category students = 7400

Seats reserved for ST Category students = 3700

(a) Percentage of seats for the students of General Category.=28200 100

49000

= 57.55%

(b)The percentage of seats students of SC Category and ST Category taken together.

Seats reserved for SC Category students = 7400

Seats reserved for ST Category students = 3700


Taken together = 7400+3700 = 11100

Therefore now the percentage of seats = 11100

49000= 22.65%

81. Prachi bought medicines from a medical store as prescribed by her doctor for

Rs 36.40 including 4% VAT. Find the price before VAT was added.

Ans: As per question,

We know that, Selling price = cost price +VAT

So, Cost price = 4

36.40 36.40100

36.40 4 0.364

36.40 1.456 .35Rs (Approx.)

82. Kritika ordered one pizza and one garlic bread from a pizza store and paid

Rs 387 inclusive of taxes of Rs 43. Find the tax%.

Ans: From the question we can figure out that the cost of one pizza and a garlic bread

inclusive of tax = Rs. 43

Therefore the cost of one pizza and a garlic bread without adding any tax = 387 -43 =

Rs.344

Therefore Tax % = 43

100344

= 100

8= 12.5%

83. Arunima bought household items whose marked price and discount % is as

follows

ITEM QUANTITY RATE DISCOUNT %

Atta 1 packet 200 16%


Detergent 1 packet 371 22.10%

Namkeen 1 packet 153 18.30%

Find the total amount of the bill she has to pay.

Ans:

Based on the data given above in the table we can say that

The rate of one packet of atta = Rs.200

Discount % = 16%

So now price= 200 -16

200100

=200-32 =Rs.168

The rate of one packet of detergent = Rs.371

Discount % =22.10%

So now the price = 371-37122.10

100 = Rs.289.009

Rate of one packet of namkeen = 153

Discount % = 18.30%

So now, price = 153-15318.30

100 =Rs.125.001

Therefore the total bill amount = 168+ 289.009+125.001 =Rs.582.01

84. Devangi’s phone subscription charges for the period 17-02-09 to 16-03-09

were as follows.

Period Amount Service tax%

17-01-09 to 23-02-09 199.75 12%


24-02-09 to 16-03-09 599.25 10%

Find the final bill amount, if 3% education cess was also charged on service tax.

Ans:

From the data given above in the table we can say that,

The amount fpr period 17-02-09 to 23-02-09 = Rs 199.75

Therefore the amount with service tax 12% = 199.75 + 12

199.75 233.72100

Rs

Amount for period 24-02-09 to 16-03-09 = Rs 599.25

Amount with service tax at 10% = 599.25+599.2510

100 =Rs 659.175

The total bill amount = Rs . 223.72 +650.175 = Rs. 882.895

Total bill amount including education cess of 3%

= 882.895+3% of 882.895

= 882.895 + 3

882.895100

= Rs. 909.39.

85. If principal = Rs 100000, rate of interest = 10% compounded half-yearly.

Find.

(a) Interest for 6 months. (b) Amount after 6 months.

(c) Interest for next 6 months, (d) Amount after one year.

Ans: From the question, Principal(P) = Rs. 100000

Rate of interest (R) = 10% compounded half yearly.

a) Interest for 6 months.


Given, n = 6 months

We know that, CI = A - P

And where for six months amount, 1200

n

RA P

1

101 100000 1

200 200

n

RA P

(As n = 1, for 6 months)

A = Rs. 105000

Now CI = A - P

CI = 105000 - 100000 = Rs.5000

(b)The amount after 6 months = Rs. 105000

(c) Interest for next 6 months.

Principal = Amount after 6 months

Therefore principal(P) = Rs.105000

Rate of interest (R)= 10%

1200

n

RA P

= 100000

1

101

200

= Rs.110250.

Compound interest, CI = A - P

CI = 110250 - 10500 = Rs. 5250

(d) Amount after one year = Rs. 110250.


86. Babita bought 160 kg of mangoes at Rs 48 per kg. She sold 70% of the

mangoes at Rs 70 per kg and the remaining mangoes at Rs 40 per kg. Find

Babita’s gain or loss per cent on the whole dealing.

Ans:

Babita bought 160 kg of mangoes = Rs. 48 per kg

So now the total amount she paid = 48 160 .7680Rs

She sold 70% of the mangoes at Rs.70 per kh.

Therefore the cost of 70% mangoes = 16070

70 . 7890100

Rs

Remaining mangoes = (100-70)% = 30%

Cost remaining at Rs. 40 per kg = 16030

40 .1920100

Rs

The total amount received after selling the mangoes = 7840+1920 = Rs. 9760

Therefore SP > CP, Hence there is a gain.

Gain = SP-CP = 9760 - 7680 =Rs,2080

Gain% = 100Gain

CP =

2080100 27.08%

7680

87.A shopkeeper was selling all his items at 25% discount. During the off season,

he offered 30% discount over and above the existing discount. If Pragya bought a

skirt which was marked for Rs 1200, how much did she pay for it?

Ans:

From the question we know that the marked price of the skirt = Rs. 1200

During normal season discount at 25% = 25

1200 .300100

Rs

The price of the skirt after discount = Rs. 1200-Rs 300= RS.900


During off season time the shopkeeper also offers discount at 30 % =

30900 270

100Rs

The price of the skirt after 30% discount = Rs. 900-270 = Rs.630.

Therefore Pragya paid Rs.630 while purchasing the skirt.

88. Ayesha announced a festival discount of 25% on all the items in her mobile

phone shop. Ramandeep bought a mobile phone for himself. He got a discount of

? 1960. What was the marked price of the mobile phone?

Ans:

Let us assume that the marked price of the mobile phone be Rs. x

We know that the festival discount on the mobile phone = 25%

The total discount which Ramandeep accepted = Rs. 1960

So according to the given data we can say that,

1960 -= x 25

100

So now, x = Rs.7840.

Hence the mared price of the mobile phone was Rs. 7840.

89. Find the difference between compound interest and simple interest on Rs

45000 at 12% per annum for 5 yr.

Ans:

From the question we know that

Principal (P) = Rs. 45000

Rate of interest (R) = 12% per annum

Time period (T) = 5 years


Simple Interest = 100

PRT=

4500 12 5

100

= Rs. 27000

Compound interest is given by,

CI = A - P

Now , A = P 1100

T

R

A = 4500

5

121

100

On calculating we get Amount, A as Rs. 79200

Therefore now the Compound interest is given by,

CI = 79200 - 45000

CI = Rs. 34200.

Therefore now the difference between SI and CI = 34200- 27000 = Rs. 7200.

90. A new computer costs Rs 100000. The depredation of computers is very high

as new models with better technological advantages are coming into the market.

The depredation is as high as 50% every year. How much will the cost of

computer be after two years?

Ans: From the question,

The cost of the new computer = Rs. 100000

The depreciation rate = 50% per annum

Time period (T) = 2 years

Now let the cost of computer after 2 years be Rs. A

A = P 1100

T

R


= 100000

2

501

100

A = Rs. 25000

Therefore the cost of the computer after 2 years will be Rs. 25000.

91. The population of a town was decreasing every year due to migration, poverty

and unemployment. The present population of the town is 6,31,680. Last year the

migration was 4% and the year before last, it was 6%. What was the population

two years ago?

Ans:As per question,

Suppose, two years ago the population = P

We know that,

1 1100 100

R RA P

So,

4 6631680 1 1

100 100P

24 47631680

25 50P

631680 25 50700000

24 47P

92. Lemons were bought at Rs 48 per dozen and sold at the rate of Rs 40 per 10.

Find the gain or loss per cent.


Cost of one dozen lemons = Rs. 48


We know that, 1 dozen = 12 pieces.

So cost of 1 lemon = 48

. .412

Rs Rs

Also 10 lemons sold for Rs. 40. So, Selling price of one lemons = 40

.410

Rs

Now the cost price of one lemon = selling price of one lemon.

So zero profit and zero loss.

93. If the price of petrol, diesel and LPG is slashed as follows:

Fuel Old prices/litre (in Rs) New prices/litre (in Rs) % Decrease

Petrol/L 45.62 40.62 -------------

Diesel/L 32.86 30.86 -------------

LPG/14.2kg 304.70 279.70 -------------

Complete the above table.

Ans: From the above table,

For per litre petrol, old price = Rs. 45.62 and

New price = Rs. 40.62

Decrement in price = Rs. 45.62 - Rs. 40.62 = Rs. 5

So, Decrease percentage 5

100 10.96%45.62

For per litre diesel, old price = Rs. 32.86 and





100 6.09%32.86

For LPG, old price = Rs. 304.70 and




100 8.20%304.70

94. What is the percentage increase or decrease in the number of seats won by A,

B, C and D in the general elections of 2009 as compared to the results of 2004?

Political Party Number of seats won in 2004 Number of seats won in 2009

A 206 145

B 116 138

C 4 24

D 11 12

Ans: For political party A,

Number of seats won in 2004 = 206


Decreased number of seats won by the party A, = 206 - 145 = 61 seats

So, Decreased percentage 61

100 29.61%206

For political party B,




Increased number of seats won by the party B, = 138 - 116 = 22 seats

So, Increased percentage 22

100 18.96%116

For political party C,



Increased number of seats won by the party C, = 24 - 4 = 20 seats


100 500%4

For political party D,



Increased number of seats won by the party D, = 12 - 11 = 1 seats


100 9.09%11

95. How many more percent seats were won by X as compared to Y in Assembly

Election in the state based on the data given below.

Party Won (out of 294)

X 158

Y 105

Z 18

W 13



Net number of seats won by the party X = 158

Net number of seats won by the party Y = 105

So, the total number of seats in election = 294

And the % of seats won by party X 158

100 53.74%294

And also, the % of seats won by party Y 105

100 35.71%294

Now, the difference of percentage = 53.74% 35.71% 18.03%

Therefore, party X won 18.03% as compared to party Y.

96. Ashima sold two coolers for Rs 3,990 each. On selling one cooler she gained

5% and on selling the other she suffered a loss of 5%. Find her overall gain or

loss % in the whole transaction.

Ans: SP of each cooler = Rs. 3990

Suppose, the CP of both coolers for Ashima = x

We know that, Profit = SP - CP

So,

53990

100x x

213990

20

x

3990 20.3800

21x Rs

And also, on another transaction of other cooler she has a loss = 5%

So,


53990

100x x

193990

20

x

3990 20.4200

19x Rs

Now, the net CP for Ashima = Rs.3800 + Rs.4200 = Rs.8000

Ashima sold both coolers = Rs.3990 2 = Rs.7980

Here, CP > SP.

So, Ashima has loss her whole transaction.

Now, Loss = Rs.8000 - Rs.7980 = Rs.20

And, loss percentage 20 1

100 % 0.25%8000 4

97. A lady buys some pencils for Rs 3 and an equal number for Rs 6. She sells

them for Rs 7. Find her gain or loss%.


cost price of some pencils = Rs. 3

For other equal no. of pencils = Rs. 6

Net selling price = Rs.7

Suppose, the lady buys ‘n’ pencils for Rs = 3. (Type - 1 pencil)

CP for one such pencil 3

n

And for ‘n’ pencils of other type, she paid = Rs 6 (Type -2 pencil)

CP for one such pencil 6

n


Net selling price of ‘2n’ pencils = Rs.7

Now, Calculation for type - 1

We know that, Gain = selling price - cost price

By using above formula,

Gain = 7 3

2n n

7 6 1

2 2n n

Also, gain percentage 100Gain

CP

1502 100 %

3 3

n

n

Now, Calculation for type - 2

We know that, Loss = cost price - selling price

By using above formula,

Loss = 6 7

2n n

12 7 5

2 2n n

Also, loss percentage 100loss

CP

51252 100 %

6 3

n

n


Net loss percentage = 125 50 75

25%3 3 3

98. On selling a chair for Rs 736, a shopkeeper suffers a loss of 8%. At what price

should he sell it so as to gain 8%?

Ans: Given, selling price of chair = Rs.736,

This led to a loss of 8%.

Suppose, the cost price of a chair = Rs. x

As per question,

Selling price = Cost price - loss

8736

100x x

92736

100

x

73600.800

92x Rs

To gain 8% profit the price should be,

8800 800 800 64 .864

100Rs

99. A dining table is purchased for Rs 3,200 and sold at a gain of 6%. If a

customer pays sales tax at the rate of 5%. How much does the customer pay in all

for the table?


Selling price of the dining table = 6

3200 3200 .3392100

Rs


Selling price with sales tax = 5

3392 3392 .3561.6100

Rs

100. Achal bought a second-hand car for Rs 2,25,000 and spent Rs 25,000 for

repairing. If he sold it for Rs 3,25,000, what is his profit percent?


Achal cost for the car = Rs. 2,25,000 + Rs. 25,000

= Rs. 2,50,000

Achal sold his car = Rs. 3,25,000

Now, profit = Rs. 3,25,000 - Rs. 2,50,000 = 75,000

So, profit percentage 100%Profit

CP

75,000100%

2,50,000

30%

101. A lady bought an air-conditioner for Rs 15,200 and spent Rs 300 and Rs 500

on its transportation and repair respectively. At what price should she sell it to

make a gain of 15%?

Ans: Actual cost price of air conditioner with transportation charge and repair charges

= Rs. 15,200 + Rs. 300 + Rs. 500

= Rs. 15,500 + Rs. 500

= Rs. 16,000

For getting gain 15% she should sell it for Rs =15

16,000 16,000100

16,000 2,400 .1,84,000Rs


102. What price should a shopkeeper mark on an article that costs him Rs 600 to

gain 20%, after allowing a discount of 10%.

Ans: Given, gain percentage = 20% and the CP of an articl = Rs. 600

Now, 600 20

.120100

Gain Rs

By using formula SP = Gain + CP

10 600 .720SP Rs

Suppose, the MP = x

Since, he allows 10% discount. So,

10720

100x x

9720

10

x

7200.800

9x Rs

103. Brinda purchased 18 coats at the rate of Rs 1,500 each and sold them at a

profit of 6%. If customer is to pay sales tax at the rate of 4%, how much will one

coat cost to the customer and what will be the total profit earned by Brinda after

selling all coats?


Net cost of 18 coats 1500 18 .27000Rs

The amount received by Brinda,

627,000 27,000 .28,620

100Rs

If customer pay sale tax = 4%


Now, CP with sale tax 4

28,620 28,620 .29764.80100

Rs

CP for 1 coat for customer 29,764.80

.1653.6018

Rs

Now, profit earned by Brinda,

.28,620 .27,000 .1,620Rs Rs Rs

104. Rahim borrowed Rs 10,24,000 from a bank for one year. If the bank charges

interest of 5% per annum, compounded half-yearly, what amount will he have to

pay after the given time period. Also, find the interest paid by him.


Suppose, amount = A

We know that, in half yearly, 2

RR and 2T T

So, for compounded half-yearly,

2 2

51 10,24,000 1

200 200

T

RA P

.10,75,840A Rs

Also, CI = A - P

.10,75,840 .10,24,000Rs Rs

.51,840Rs

105. The following items are purchased from showroom:

T-Shirt worth Rs 1200. Jeans worth Rs 1000. 2 Skirts worth Rs 1350 each.

What will these items cost to Shikha if the sales tax is 7%?



Net cost .1200 .1000 .1350 .3550Rs Rs Rs Rs

Shikha have to pay sale tax 7%

Now, the net amount to pay 7

3550 3550 .3798.5100

Rs

106. The food labels given below give information about 2 types of soup: cream of

tomato and sweet corn. Use these labels to answer the given questions. (All the

servings are based on a 2000 calorie diet.)

Sweet Corn

Nutrition Facts

Serving Size 1 cup (240ml)

About 2 serving per Container

Cream of Tomato

Nutrition Facts Serving

Size 1 cup (240ml)

About 2 serving per Container

Amount Per Serving

Calories 90 Calories from Fat 9

Amount Per Serving

Calories 100 Calories from Fat 20

% Daily

Value*

Total Fat 2g 2%

Saturated Fat-0g 0%

Cholesterol 0mg 0%

Sodium 540mg 22%

Total Carbohydrate 17g 6%

Dietary Fibre 3 gram 14%

% Daily

Value*

Total Fat 2g 3%

Saturated Fat-1.5g 6%

Cholesterol 10mg 3%

Sodium 690mg 29%

Total Carbohydrate 17g 6%

Dietary Fibre 4 gram 18%


Sugar 5g

Protein 3g

Sugar 11g

Protein 2g

Vitamin A 30% Vitamin C 10% Vitamin A 20% Vitamin C 20%

Calcium 2% Iron 6% Calcium 0% Iron 8%

*Percent Daily Values are based on a

2,000 calorie diet.

*Percent Daily Values are based on a

2,000 calorie diet.

(a) Which can be measured more accurately : the total amount of fat in cream of

tomato soup or the total amount of fat in sweet corn soup? Explain.

(b) One serving of cream of tomato soup contains 29% of the recommended daily

value of sodium for a 2000 calorie diet. What is the recommended daily value of

sodium in milligrams? Express the answer upto 2 decimal places.

(c) Find the increased percent of sugar consumed if cream of tomato soup is

chosen over sweet corn soup.

(d) Calculate ratio of calories from fat in sweet corn soup to the calories from fat

in cream of tomato soup.


a) Serving size of one cup of sweet corn = 240mL

Net fat = 2g on 2%

The total amount of fat in sweet corn soup,

2240 4.8

100g

Now, for one serving 4.8

2.42

g


Given, serving cost of one cup of tomato cream,

3240 7.2

100g

Now, for one serving 7.2

3.62

g

b) According to the question,

29% of 2000 calories = 690 mg

c) The increase percent of sugar consumed = 11g - 5g = 6g

So, increased percentage 6

100% 120%5

d) fat in sweet corn soup in calories = 9

And fat in cream tomato soup in calories = 20

The ratio 9

20

107. Music CD originally priced at Rs 120 is on sale for 25% off. What is the

S.P.? Sonia and Rahul have different ways of calculating the sale price for the

items they bought.


As you work on the next problem, try both of these methods to see which you

prefer.


Original price of CD = Rs. 120

25% discount on Rs. 120.

If the sale is applicable, Discount 25

120 .30100

Rs

So, selling price after discount = Rs. 120 - Rs. 30 = Rs. 90

108. Store A and Store B both charge Rs 750 for a video game. This week the

video game is on sale for Rs 600 at Store B and for 25% off at Store A. At which

store is the game less expensive?


20% discount at store A. So,

Selling price at store A 20

750 750100

750 150

.600Rs

Given, selling price at store B = Rs.600

So, both are equally expensive.

109. At a toy shop the price of all the toys is reduced to 66% of the original price.

(a) What is the sale price of a toy that originally costs Rs 90?

(b) How much money would you save on a toy costing Rs 90?


a) When price reduced to 66% of the original price,


Then the price 66

90 90 .30.6100

Rs

b) Saved money 66

90 .59.4100

Rs

110. A store is having a 25% discount sale. Sheela has a Rs 50 gift voucher and

wants to use it to buy a board game marked for Rs 320. She is not sure how to

calculate the concession she will get. The sales clerk has suggested two ways to

calculate the amount payable.

Method 1: Subtract Rs 50 from the price and take 25% off the resulting price.

Method 2: Take 25% off the original price and then subtract Rs 50.

a. Do you think both the methods will give the same result? If not, predict which

method will be beneficial for her.

b. For each method, calculate the amount Sheela would have to pay. Show your

work.

c. Which method do you think stores actually use? Why?


a) In method 1,

Rs. 320 - Rs. 50 = Rs. 270

25% discount on Rs. 270 25

270 270 .202.5100

Rs

In method 2,

25% discount on Rs. 320 25

320 320 .240100

Rs

Price = Rs. 240 - Rs. 50 = Rs. 190

So, method 2 is beneficial for her.

b) In method 1, Amount paid = Rs. 202.5


In method 2, Amount paid = Rs. 190

c) Method 1. This method shows actual discount in loss.

111. Living on your own: Sanjay is looking for a one-bedroom apartment on rent.

At Neelgiri apartments, rent for the first two months is 20% off. The one

bedroom rate at Neelgiri is Rs 6,000 per month. At Savana apartments, the first

month is 50% off. The one bedroom rate at Savana apartments is Rs 7000 per

month. Which apartment will be cheaper for the first two months? By how

much?


Rent for first two months,

202 6000 6000 .9600

100Rs

By comparison of Savana apartment, it offers 50% off for her first month, where the

rent for bedroom .7000 /Rs month

507000 7000 .3500

100Rs

So, the rent for two months in Savana apartment,

3500 7000 .10500Rs

Therefore, Neelgiri apartment will be cheaper by,

= .10500 .9600 .900Rs Rs Rs

112. For an amount, explain why, a 20% increase followed by a 20% decrease is

less than the original amount.

Ans: Suppose, the original price = x

20% increase in original price =20 6

100 5

xx x


Now, 20% decrease in 6 6 20 6

5 5 100 5

x x x

30 6 24

25 25 25

x x x

So the decreased price is less than the original price because decrement is calculated

on increased price and increment is calculated on original price. So Decrement is more

than increment.

113. Sunscreens block harmful ultraviolet (UV) rays produced by the sun. Each

sunscreen has a Sun Protection Factor (SPF) that tells you how many minutes

you can stay in the sun before you receive one minute of burning UV rays. For

example, if you apply sunscreen with SPF 15, you get 1 minute of UV rays for

every 15 minutes you stay in the sun.

1. A sunscreen with SPF 15 allows only 1

15 of the sun’s UV rays. What percent of

UV rays does the sunscreen abort?

2. Suppose a sunscreen allows 25% of the sun’s UV rays.

a. What fraction of UV rays does this sunscreen block? Give your answer in

lowest terms.

b. Use your answer from Part (a) to calculate this sunscreen’s SPF. Explain how

you found your answer.

3. A label on a sunscreen with SPF 30 claims that the sunscreen blocks about

97% of harmful UV rays. Assuming the SPF factor is accurate, is this claim true?

Explain.

Ans:i) According to the question, 14

15 of the sun’s UV rays aborted by sunscreen.

In percentage

14

15 100 93.33%1

ii) a) Lowest fraction of blocked UV rays,


= 100 - 25 =75% = 75 3

100 4

b) Sunscreen allows 25% or 3

4 of UV rays. Means, it protects UV rays

3 11

4 4

Therefore, its SPF = 4

iii) The given statement is false.

114. A real estate agent receives Rs 50,000 as commission, which is 4% of the

selling price. At what price does the agent sell the property?

Ans: Let the selling price = .Rs x

According to question,

4% of x is equal to Rs. 50,000.

450,000

100x

25 50,000x

12,50,000x

115. With the decrease in prices of tea by 15% Tonu, the chaiwallah, was able to

buy 2 kg more of tea with the same Rs 45 that he spent each month on buying tea

leaves for his chai shop. What was the reduced price of tea? What was the

original price of tea?



Suppose, purchased tea = y kg

Price of tea per kg = Rs. x

Discount 15% per kg,

15 85

100 100

xx x

A chaiwallah can buy 2 kg extra with 15% of discount.

But without discount, xy = 45 .....(i)

And 85

2 45100

xy ii

By solving equation (i) and (ii):

85 85 245

100 100

xy x

85 2 85 4545

100 100

x

170 4500 85 45x

45 1 00 45 85 45 1 53.97

170 170x per kg

So, the reduced price = 85 3.97

3.37 100

per kg


116.116 Below is the report card of ViditAtrey. Vidit’s teacher left the last

column blank. Vidit is not able to make out, in which subject he performed better

and in which he needs improvement. Complete the table to help Vidit know his

comparative performance.Assessment report for- 2009-2010

Assessment Report for 2009-2010

Class : 9B Name : Vidit Atrey Date : 31 March 2010

S.No Subject Internal assessment Examination Total Final%

1. English Literature 20/25 82/100 102/125

2. English Language 22/25 91/100 113/125

3. Hindi Literature 18/25 67/75 85/100

4. Hindi Language 16/25 68/75 84/100

5. Mathematics 42/50 88/100 130/150

6. Sanskrit 14/20 75/100 99/120

7. Physics 45/50 90/100 135/150

8. Chemistry 41/50 82/100 123/150

9. Biology 43/50 87/100 130/150

10. History and Civics 19/25 68/75 87/100

11. Geography 17/20 71.5/80 88.5/100

Ans:

From the data which is been given in the table , we can calculate the final percentage

of each subjects.

1. English Literrature = 102 408

100 81.6%125 5

2. English language = 113 452

100 90.4%125 5

3. Hindi literature = 85

100 85%100

4. Hindi language = 84

100 84%100

5. Mathematics = 130 1300

100 150 15

86.67%


6. Sanskrit = 89 890

100 74.16%100 5

7. Physics = 135 1350

100 90%150 15

8. Chemistry = 123

100 82%150

9. Biology= 130 1300

100 86.66%150 15

10. History and Civics = 87

100 87%100

11. Geography = 88.5 452

100 88.5%100 5

117.Sita’s practicing basket ball. She has managed to score 32 baskets in 35

attempts. What is her success rate in percentage?

Ans:

It is given that Sita managed to score 32 baskets in 35 attempts.


Now her success rate will be = 32

10035

=91.428%= 91.43%

118. During school hours, Neha finished 73% of her homework and Minakshi

completed 5

8 of her, homework. Who must finish a greater per cent of 8

homework?

Ans:

It is given in the question that during school hours, Neha finished 73% of her

homework and Minakshi completed 58 of her homework.

In percentage Neha finished her homework = 73%= 73

100

Simillarly Minakshi completed 5

8 of her homework.

Homework left from Minakshi = 1- 5

8 =

3

8

In percentage = 3

100 37.58 %

Homework left for Neha = (100-73) = 27% = 27

100

Hence from the calculation we can say that Minashi finishes a greater percentage of

homework compared to Neha.

119. Rain forests are home to 90000 of the 250000 identified plant species in the

world. What per cent of the world’s identified plant species are found in rain

forests?

Ans:

It is given that rain forests are home to 90000 of the 250000 identified plant species in

the world.


Percentage = 90000 900

100 36% 250000 25

120.Madhu’s room measures 6m x 3m. Her carpet covers 8 m2. What per t cent

of floor is covered by the carpet?

Ans:

From the question we know that,

Madhu’s room measures = 6m 3 m

Area of the room = 6 3 = 18 2m (From area of the rectangle = l b )

Madhu’s carpet covers = 8 2m

Therefore area covered by the carpet in percentage = 8

100 44.44%18

121.The human body is made up mostly of water. In fact about 67% of a person

total body weight is water. If Jyoti weights 56 kg, how much of her weight is

water?

Ans:

From the question we can say that

Jyoti’s weight = 56 kg

We know that 67% of a person total body weight is water

Water in Jyoti body = 67

56 37.52 100

kg

122.The per cent of pure gold in 14 carat gold is about 58.3%. A 14 carat gold

ring weights 7.6 grams. How many grams of pure gold are in the ring?

Ans:


The percentage of gold in 14 carat gold = 58.3%

Weight of 14 carat gold = 7.6 g

Pure gold in 14 carat gold of 7.6 g = 7.6 58.3 443.08

4.431 100 100

g

Hence, pure gold in 7.6 g 0f 14 carat gold is equal to 4.431 g.

123.A student used the proportion 100 325n to find 5% of 32. What did the

student do wrong?

Ans:It is given in the question that the student used the proportion 100 325n to find 5%

of 32 , which is an incorrect approach.

5% of 32 will be calculated as = 5

32100

=1.6

124.The table shows the cost of sunscreen of two brands with and without sales

tax. Which brand has a greater sales tax rate? Give the sales tax rate of each

brand?

Cost in Rs Cost + Tax in Rs

1 X (100 g) 70 75

2 Y (100 g) 62 65

Ans:

From the question we can say that,

The brand X sunscreen cost = Rs. 70

With sales tax = Rs.75

Sales tax paid = Rs.75-Rs.70 = Rs.5

The cost of rand Y sunscreen = Rs. 62


UncludinG sales tax = Rs.65

Sales tax for Y = Rs.65 - Rs. 62 =Rs.3

Therefore brand X sales tax is more compared to brand Y.

Sales tax for brand X = 5

100 7.14%70

Sales tax brand Y = 3

100 4.84%62

NCERT Exemplar Solutions For Grade 8 Mathematics Chapter ...

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