STUDY NOTES FOR SSC AND OTHER EXAM

STUDY NOTES FOR SSC AND OTHER EXAM

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Important Formulas and Shortcuts to solve

Percentage

Percentage is a very basic and important topic for

Quantitative Aptitude as you can solve other topics

speedily with its help. These formulas and shortcuts will

be helpful for your upcoming Exams like Railway and

SSC 2018.

Percentage (%)

Percent sign

The percent sign is the symbol: %

It is written to the right side of the number: 50%

Percentage Definition

The percentage is a value that represents the proportion

of one number to another number.

Percentage is per-cent which means parts per hundred

(1/100).

If we have to convert percentage into fraction then it

is divide by 100.

Example:

If we write 45% then its equal to 45/100 or in fraction

9/20 or in decimal 0.45

If we have to convert fraction into percentage we

have to multiply it with 100.

Example:

If we write 3/5 in fraction it is equal to 60% = 3

1005

= 60.

Convert Percentage into Decimal:

20% = 20

100= 0.5

Convert Decimal Into Percentage:

0.25 = (0.25 × 100) % = 25%

1.50 = (1.50 × 100) % = 150%

Majorly used values shown in Percent, Decimal and

Fraction

This table will help you solve questions very fast and

easily. Try to remember these fractions because it

will save a lot of time in your examination.

Percent

Decim

al

Fracti

on

1% 0.01 1/100

5% 0.05 1/20

10% 0.1 1/10

12 ½% 0.125 1/8

20% 0.2 1/5

25% 0.25 ¼

133 %

3 0.333 1/3

50% 0.5 ½

75% 0.75 ¾

80% 0.8 4/5

90% 0.9 9/10

99% 0.99 99/10

0

100% 1

125% 1.25 5/4

150% 1.5 3/2
















































































200% 2

Types of Formulas and Short Tricks

Type 1:

Percentage Increase/Decrease:

If the price of a commodity increases by R%, then

the reduction in consumption so as not to increase

the expenditure is:

R100%

100 R

If the price of a commodity decreases by R%, then

the increase in consumption so as not to decrease the

expenditure is:

R100%

100 R

If the value of a number is first increased by a% and

later decreased by a%. Then the net effect is always

decreased which is equal to a% of a and is written is

2

%100

a

Type 2:

Results on Population:

Let the population of a town be P now and suppose it

increases at the rate of R% per annum, then:

1.Population after n years =

nR

P 1100

2.Population n years ago = n

P

R1

100

Type 3:

Results on Depreciation:

Let the present value of a machine be P. Suppose it

depreciates at the rate of R% per annum. Then:

1. Value of the machine after n years =

nR

P 1100

2. Value of the machine n years ago = n

P

R1

100

3. If A is x% more than B, then B is less than A by=

x100%

100 x

4. If A is x% less than B, then B is more than A by=

x100%

100 x

Note:

For two successive changes of x% and y%, net change =

{x + y +xy

100} %

5 Some basic Questions with Short Tricks on

Percentage:

Question 1: If the radius of a circle is increased by

50%, its area is increased by

(1) 125% (2) 100%

(3) 75% (4) 50%

Solution:

Let the old area be 100%.

50% increase means 150%

So, 100 × 150% × 150% (because of 2 dimensional)

3 3

100 2252 2

Increase = 225 – 100= 125%

Short Trick:

Formula: a + b + a b

100

= 50% + 50% + 50% of 50%

= 100% + 25% = 125%

Question 2:

The price of an article is reduced by 25% but the

daily sale of the article is increased by 30%. The net

effect on the daily sale receipt is

(1) 1

2 %2

Increase

(2) 1

2 %2

Decrease

(3) 2% Increase

(4) 2% Decrease

Solution:








































































Let the price of the article be Rs.100 and the daily sale

be 100 units

Revenue per day = 100 × 100 = Rs.10000

Case II:

New receipts = 75 x 130 = Rs.9750

Decrease = (10000 – 9750) = 250

% decrease = 250 1

100 2 %10000 2

Short Trick 1:

Let the daily sale is 100

So, 75 130

100 97.5100 100

Means, 100 – 97.5 = 2.5 % decrease

Decreases by 2.5%

Short Trick: 2:

= – 25% + 30 % + (– 25%) of (30%)

= 2.5 % decrease

Question 3:

In a test consisting of 80 questions carrying one mark

each, Ankita answered 65% of the first 40 questions

correctly. What percent of the other 40 questions

does she need to answer correctly to score 75% on

the entire test?

(1) 60 (2) 80

(3) 75 (4) 85

Solution:

According to question,

(x% of remaining 40 ques.) + (65% of already done 40

question) = 75% of total 80 questions

x 65 7540 40 80

100 100 100

40x 2600 6000

100 100

40x + 2600 = 6000

40x = 3400

x = 85 %

Simple Way:

65% of 40 questions = 65

40100

= 26 questions

Thus, she gets 26 marks

But she needs to score 75% of 80 = 75

80100

= 60

marks

Req. marks = 60 – 26 = 34 marks

Now, x% of 40 = 34

34 100

x 85%40

Question 4:

If Ravi's salary is 25% more than Raju's salary, then

the percentage by which Raju's salary is less than

Ravi's salary is

(1) 15 (2) 20

(3) 25 (4) 32

Solution:

Ravi's = 125

100× Raju's salary =

5

4× Raju's salary

This means if Raju's salary is Rs.4 then Ravi's salary in

Rs.5.

They Required % = 5 4

100 20%5

Short Trick:

Raju Ravi

25100 20%

125

Question 5:

In a village, each of the 60% of families has a cow;

each of the 30% of families has buffalo and each of

the 15% of families has both a cow and a buffalo. In

all there are 96 families in the village. How many

families do not have a cow or a buffalo?

(1) 20 (2) 24

(3) 26 (4) 28

Solution:

Families have cow = + 60%

Families have buffalo = + 30%

Families have both = - 15%

Families have a cow or a buffalo = 75%

Families don't have any cow or a buffalo

= 25% of 96 = 24

Solved Questions:

Question 6:

If ram earns 25% more than Shyam then what %

less does Shyam earn than ram?

125%

4

It means Shyam income is 4 and Ram income is 5

So ram is % less than Shyam

= 1 100 20%5

Question 7:








































































A's income is 10% more than B's income. How much

per cent is B's income less than A's income?

Solution:

Let B's Income = Rs.100

A's income = 100 110110

100

Required percentage =

10 1100 9 %

110 11

Question 8:

If ram earns 𝟏𝟔𝟐

𝟑% more than Shyam what % less

does Shyam earn than Ram?

2 116 %

3 6

Shyam = 6 and Ram = 7

Shyam is % less than Ram

= 1 2100 14 %

7 7

Question 9:

Sixty – five percent of a number is 21 less than three

– fourth of that number. What is the number?

Solution:

Three fourth = ¾ = 75%

75% - 65% = 21

10% = 21

100% = 210

Question 10:

If 𝟔𝟔𝟐

𝟑% of a no. is added with itself then result

becomes 3900. Find the original number?

Solution:

2 266 %

3 3

It means 3 is the original number

And 2 is added to the number then it becomes 5 and

5 unit = 3900

1 unit = 780

3 unit = 2340

Question 11:

If 96 is added in a number then number becomes

157𝟏

𝟕% of itself. Find the numbers?

Solution:

1 1 114157 % 100 57 1

7 7 7 7

It means 7 is the original number and after adding 96 it

becomes 11 that means

4 unit = 96

1 unit = 16

7 unit = 112

Question 12:

If the sides of a square is increased by 40% find the

percentage change in its area?

100

xyx y

40 4040 40

100

80 16

96

Question 13:

If the radius of a circle is increased by 25% then find

the percentage change in its area ?

Solution:

125%

4

It mean we can say radius of circle is 4

And new radius is 5

So area of original circle = 16

So new area of original circle = 25

Percentage change in area =

25 16 9100 100 56.25%

16 16

Question 14:

If the base radius of a right circular cylinder is

increased by 40% and its height is reduce by 37.5%

then find the percentage change its volume?

Solution:

2 340% ,37.5%

5 8

It means original radius is 5 and original height is 8

Volume of cylinder = 25 8 200

New radius is 7 and new height is 5

New volume of cylinder = 49 5 245

Percentage change in area = 245 200100 22.5%

200








































































Question 15:

If the length of the rectangle is increased by 37𝟏

𝟐%

and its breadth is decreased by 16𝟐

𝟑%. Find the

approximate % change in its area?

Solution:

1 3 2 137 % ,16 %

2 8 3 6

It means original length of rectangle is 8 and original

breadth of rectangle is 6

Area of rectangle = 48

New length of rectangle is 11

New breadth of rectangle is 5

Area of rectangle is 55

So percentage change in area

= 55 48100 14.58%

48

Question 16:

A man saves a certain parts of his income every

month, so that he can purchase a car in one year. By

what percent he must increase in his saving, so that

he can purchase the same car in nine month?

Solution:

Let the amount of the car is 36

So he saves 3 rupees per month if he has to purchase to

it in 12 month

If he has to purchase it in 9 month

So he saves 4 rupees per month

His saving increased by

4 3 1100 33 %

3 3

Question 17:

The price of sugar is increased by 16𝟐

𝟑% and the

consumption of a family is decreased by 20%. Find

the % change in expenditure?

Solution:

2 116 %

3 6 1

20%5

It means the original price of sugar is 6 and

consumption of family is 5

Total expenditure is 30

And new price of sugar is 7 and new consumptions is 4

Total expenditure is 28

Percentage change in expenditure is

30 28 200 2100 6 %

30 30 3

Question 18:

The sale of a cinema ticket is increased by 57𝟏

𝟕% and

the price of ticket is increased by 16𝟐

𝟑%. Find the

change in his revenue?








































































Solution:

1 457 %

7 7 2 1

16 %3 6

It means no. of sale of cinema ticket is 7 and original

price of ticket is 6

Therefore total revenue is 42

New sale of ticket is 11

New price of ticket is 7

New revenue is 77

Percentage change in its revenue is

77 42 35100 100 83.33%

42 42

Question 19:

A man can type 20 line in 10 minute but he leaves

8% margin on each line. In how many time he will

type 23 page with 40 lines on each page on which he

leaves 25% more margin of before

Solution:

We know that

20 line in 10 minute

It means 2 lines per minute

If he leaves 8% margin that means

2 × 92 line/minute

But he has to type 23 page with 40 lines leaves 25%

more margin of before

Which means

23 × 40 × 90 = 2 × 92 × x

x = 450 min

Question 20:

If the income tax is increased by 19% then net

income is reduced by 6%. Find the rate of income

tax?

Solution:

19 6

100 100

6

19

tax NI

tax

NI

Total income is 6 + 19 = 25

Rate of income tax is

6100 24%

25

Question 21:

Deepak spends 40% of his salary on house rent, on

remaining 10% spends on travels , on remaining 16𝟐

𝟑

% spends on food and remaining is saved. If he saved

Rs. 6750 what amount he spent on food?

Solution:

Let the income be 100

House rent = 40

Remaining = 60

Travel = 60 × 10% = 6

Remaining = 54

Food = 54 × 16.66% = 9

Remaining = 45

45 = 6750

1 = 150

Amount spent on food

150 × 9 = 1350

Question 21:

In an examination 35% is passing marks one

candidate obtain 135 marks and failed by 40 marks

then find the maximum marks?

Solution:

35% = 135 + 40

100% = 175100 500

35

Question 22:

Rohit obtained 480 marks out of 600 and Mohit

obtained 560 marks out of 800. Whose performance

is better and how much %?

Solution:

Rohit got = 480

600 x 100 = 80 %

Mohit got = 560

800 x 100 = 70 %

Rohit performance is better.

% better = 10

70 x 100 = 14

2

7 %

Question 23:

In an election between two candidates, 65 votes were

declared invalid one candidate get 52% votes and

win by 98 votes. Find the total number of votes?

Solution:

Winner 52% Looser 48%

4% = 98

100% = 2450

Valid vote = 2450

Total vote = 2450 +65 = 2515

Question 24:

The length and breadth of rectangle is increased by

30% and 20% respectively, so find the net % change

in its area?

Solution:

Net % change = x + y + x × y

100

= 30 + 20 + 30×20

100

= 56%




































































Question 25:

A number is mistakenly divided by 10 instead of

being multiplied by 10.What is the percentage error

in the result?

Solution:

Let the number is 10.

Actual result = 10 x 10 = 100

Wrong result = 10

10 = 1

% change = 100−1

100 x 100 = 99%

Question 26:

The numerator of a fraction is increased by 400%

and denominator is increased by 500%, so the

resultant fraction is 15/22. Find the original fraction?

Solution:

500% 𝑜𝑓 𝑥

600% 𝑜𝑓 𝑦 = 15

22

5𝑥

6𝑦 = 15

22

Original Fr/action 𝑥

𝑦 = 15×6

22×5

Original Fraction = 9

11

Question 27:

A, B and C are three persons. A earned 40% more

than B and B earned 20% less than C, so what %

more earned A than C.

Solution:

A B C

112 80 100

A more earned than C = 112 – 100 = 12

% more earned = 12 100

100

= 12 %

Question 28:

Due to reduction of 20% in the price of apples

enables a person to purchase 16 apples more for

Rs.320, so find the reduced rate of 10 apples?

Solution:

Reduced rate = 320×20

100 = 64

Reduced rate of 1 apple = 64

16 = Rs.4

Reduced rate of 10 apples = 4 x10

= Rs.40

Question 29:

A mixture of 40 litres of milk and water contains

10% water. How much water should be added, so

water may be 20% in the new mixture?

Solution:

40×10

100= 4 lit.

80% = 36

1% = 36

80

20% = 36

80× 20= 9 Lit.

Req. water = 9 – 4 = 5 lit.

Question 30:

Fresh fruit contains 68% water and dry fruit

contains 20% water. How much dry fruit can be

obtained from 100 kg. of fresh fruit?

Solution:

Fruit content in 100 kg. of fresh fruits = 100×32

100

= 32 kg.

Since, dry fruits contain 80% fruit content,

80% = 32

1% = 32

80

100% = 32

80× 100= 40 kg.

EXPECTED QUESTIONS:

Q.1. Vimal bought a watch costing Rs.1404 including

sales tax at 8%. He asked the shopkeeper to reduce

the price of the watch so that he can save the amount

equal to the tax. The reduction of the price of the

watch is?

(A) Rs.108 (B) Rs.104

(C) Rs.112 (D) Rs.120

Solution:(B)

1.08x = 1404, x = 1300

The reduction of the price of the watch = 104

Q.2. A Sales Executive gets a commission on total sales at

8%. If the sale is exceeded Rs.10, 000 he gets an

additional commission as a bonus of 4% on the

excess of sales over Rs.10, 000. If he gets the total

commission of Rs.950, then the bonus he received is?

(A) 40 (B) 50

(C) 36 (D) 48

Solution:(B)

Commission up to 10000 = 8

10000 800100

Ratio = 2x: x; Commission = 2x, Bonus = x;

Bonus = 1 1

950 800 150 503 3




































































Q.3. In a College there are 1800 students. Last day except 4%

of the boys all the students were present in the college.

Today except 5% of the girls all the students are present

in the college, but in both the days number of students

present in the college, were same. The number of girls

in the college is?

(A) 1000 (B) 400

(C) 800 (D) 600

Solution:(C)

From Options; let Number of girls = 800

Number of boys = 1000

96% of 1000 + 800 = 95% of 800 + 1000

Q.4. In a library 60% of the books are in Hindi, 60% of the

remaining books are in English rest of the books are in

Malayalam. If there are 4800 books in English, then the

total number of books in Malayalam are?

(A) 3400 (B) 3500

(C) 3100 (D) 3200

Solution:(D)

Let there are x books in the library.

Hindi books = 60% of x = 60x

100= 0.6X

Remaining Books = x - 0.6x = 0.4x

English books = 40% of reaming books

= 60% of 0.4x = 0.24x.

Malayalam Books = x - 0.6x - 0.24x = 0.16x

Given, 0.24x = 4800

x = 4800/0.24 = 20000

Malayalam Books = 0.16x = 0.16 × 20000 = 3200.

Q.5. 80% of a small number is 4 less than 40% of a larger

number. The larger number is 125 greater than the

smaller one. The sum of these two numbers is

(A) 325 (B) 345

(C) 355 (D) 365

Solution:(C)

Smaller number = x; Larger number = y

0.8x + 4 = 0.4y

4y – 8x = 40

y – x = 125

x = 115; y = 240

x + y = 355

Q.6. In a private company 60% of the employees are men

and 48% of the employees are Engineer and 66.6% of

Engineers are men. The percentage of women who are

not engineers is?

(A) 60% (B) 50%

(C) 55% (D) 65%








































































Solution:(A)

Men = 600x, Women = 400x

Total engineers = 480x,

Male engineers = 480x × 0.66 = 320x

Women who are Engineers = 160x

Women who are not Engineers = 400x – 160x = 240x

Required percentage = 240

100400

= 60%

Q.7. Initially, Suresh has Rs.200 in his paytm wallet then he

increased it by 20%. Once again he increased his

amount by 25%. The final value of money in his wallet

will be how much % greater than the initial amount?

(A) 40% (B) 50%

(C) 80% (D) 60%

Solution:(B)

200 + 20% of 200 = 240

240 + 25% of 240 = 300

Required percentage = 300 200

100200

= 50%

Q.8. Mr. Ramesh gives 10% of some amount to his wife and

10% of the remaining to hospital expenses and again

10% of the remaining amount to charity. Then he has

only Rs.7290 with him. What is the initial sum of

money with that person?

(A) Rs.8000 (B) Rs.9000

(C) Rs.10000 (D) Rs.20000

Solution:(C)

Remaining amount = x × 0.9 × 0.9 × 0.9

0.729x = 7290

x = 10000

Q.9. Initially, a shopkeeper had "x" pens. A customer bought

10% of pens from "x" then another customer bought

20% of the remaining pens after that one more customer

purchased 25% of the remaining pens. Finally,

shopkeeper is left with 270 pens in his shop. How many

pens were there initially in his shop?

(A) 200 (B) 800

(C) 400 (D) 500

Solution:(D)

x × 0.9 × 0.8 × 0.75 = 270

x = 270 10000

9 8 75

= 500

Q.10. The cost of packaging of the oranges is 20% the cost of

fresh oranges themselves. The cost of oranges increased

by 30% but the cost of packaging decreased by 50%,

then the percentage change of the cost of packed

oranges, if the cost of packed oranges is equal to the

sum of the cost of fresh oranges and cost of packaging

(A) 14.5% (B) 16.66%

(C) 14.33% (D) 13.66%

Solution:(B)

Let initial Cost of fresh, oranges = 100.

Packaging cost = 20.

Initial total cost = 100 + 20 = 120

After increasing in cost of fresh mangoes 30%,

Cost of fresh mangoes = 130

And cost of packing go down by 50 %

So, Cost of packing = 10.

Total cost = 130 + 10 = 140.

Increased cost = 140 - 120 = 20.

% increased = 20 100

120

= 16.66%.

Q.11. Cost Price of two laptops is same. One of the laptops is

sold at a profit of 15% and the Selling Price of another

one laptop is Rs.3400 more than the first one. The net

profit is 20%. What is the Cost Price of Each laptop?

A.36000 B.40000

C.48000 D.34000

Solution:(D)

(2x*1.15) + 3400 = 2x*1.20

2.4x – 2.3x = 3400

x = 34000

Q.12. In an office there are 40% female employees. 50% of

the male employees are UG graduates. The total 52% of

employees are UG graduates out of 1800 employees.

What is the number of female employees who are UG

graduates?

(A) 362 (B) 412

(C) 396 (D) 428

Solution:(C)

Total employees = 1800

Female employees = 40%

Male employees = 60%




































































50% of male employees = UG graduates = 30%

Female employees who are UG graduates = 22%

22% of 1800 = 396

Q.13. Ravi got 70% in English and 56% in Biology and the

maximum marks of both papers is 100. What percent

does he score in Maths, if he scores 60% marks in all the

three subjects? Maximum Marks of Maths paper is 200.

(A) 30% (B) 40%

(C) 45% (D) 57%

Solution:(D)

70 + 56 + x = 60% of all three subjects

70 + 56 + x = 60% of 400

x = 240 – 126 = 114

% = 114

100200

= 57%

Q.14. Ankita is 25 years old. If

Rahul’s age is 25% greater than that of Ankita then how

much percent Ankita’s age is less than Rahul’s age?

(A) 40% (B) 35%

(C) 10% (D) 20%

Solution:(D)

Percentage decrease = 25

100125

= 20%

Q.15. Mr. Ravi’s salary was reduced by 25% for three months.

But after the three months, his salary was increased to

the original salary. What is the percentage increase in

salary of Mr.Ravi?

(A) 33.33% (B) 42.85%

(C) 28.56% (D) 16.66%

Solution: (A)

Percentage increase = 25

10075

= 33.33%





































































STUDY NOTES FOR SSC AND OTHER EXAM

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