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1

S.No. Topic Page

3. Profit and Loss 2

4. Exercise-1 8




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CHAPTER-2-PROFIT & LOSS

Profit and Loss questions are simply applied

percentage questions. For all practical purposes, if

you understand the basics of percentage, you are

ready to solve any question of profit and loss.

SOME BASIC DEFINITIONS

Cost Price

The price at which you buy anything is Cost price.

Selling Price

The price at which an article is sold is called selling

price.

Profit or Gain

When an article is sold for more than what it costs

we say there is a profit or gain. Thus,

Profit = S.P. – C.P.

% Profit = SP−CP

CP× 100

Note: Unless mentioned otherwise in the question,

the profit percentage is always calculated on the

cost price of the item.

Loss

When an article is sold for less than what it costs we

say there is loss. Thus,

Loss = C.P. – S.P.

% loss = CP−SP

CP× 100


the loss percentage is always calculated on the cost

price of the item.

Marked Price

List price or the price printed on the article is known

as Marked Price (abbreviated as M.P.)

Discount

Sometimes dealers allow some reductions on list

price or marked price. This reduction is known as

discount.

% Loss = MP−SP

MP× 100


the discount percentage is always calculated on the

marked price of the item.

Premium

In some situations, dealers are able to sell their

goods at a price higher than the stated Marked

price. The difference between the the higher selling

price, in this case, and marked price is called as

premium.

% premium = SP−MP

MP× 100


the premium percentage is always calculated on the

marked price of the item.

QUESTIONS ON BASIC CALCULATIONS

Example- 1. If C.P.=125, S.P. = 96, then loss = ?

Loss= CP-SP = 125 – 96 = Rs 29

Example-2 If C.P.=112, S.P.=132, then Gain =?

Gain = SP-CP = 132-112 = Rs 20

Example-3 If C.P.=120, S.P. = 90, then loss % = ?

% loss = CP−SP

CP× 100 =

120−90

90× 100. = 33

1

3 %

USEFUL INTERPRETATION OF PROFIT AND LOSS

For all practical purposes, profit % stands for the

percentage by which SP is greater than CP and loss

stands for the percentage by which SP is less than

CP

Why?

From our discussion of the percentages, we know

that the percentage by which A is greater than B is

given by 𝐴−𝐵

𝐵× 100

In the above expression, replace A by SP and B by CP

and you will get the formula for profit percentage.

Therefore,

if the profit percent is 10%, SP is more than CP by

10%, therefore

(i)SP = 1.1CP

(ii) SP = CP. + 10% of CP

If the profit percent is 20%, SP is more than CP by

20%, therefore,

(i)SP = 1.2CP

(ii) SP = CP. + 20% of CP

If loss percent is 10%, SP is less than CP by 10%,

therefore,

(i)SP = 0.9 CP

(ii) SP = CP. - 10% of CP

In general

SP =100±R

100× CP




3

Where R is positive if there is a profit and R is

negative in case of a loss.

IMPORTANT POINTS

If you sell two items which have the same CP,

gaining R% on one and losing R% on the other,

overall there is no profit or loss.

If you sell two items at the same SP, gaining R%

on one and losing R% on the other, overall there

is always a loss = R2

100 %

Example-4 The selling price of a commodity is Rs

720. If the trader earns a profit of 20%, what is his

cost price?

Solution:

Since the trader earns a profit of 20%

SP = 100+20

100× CP. = 720

1.2 CP = 720

CP = Rs 600

[Ans: Rs 600]

Example-5 The selling price of a commodity is Rs

720. If the trader earns a loss of 10%, what is his cost

price?

Solution:

Since the trader earns a loss of 10%

SP = 100−10

100× CP. = 720

0.9 CP = 720

CP = Rs 800

[Ans: Rs 800]

Example-6 A man buys 6 items for a rupee and sold

at the rate of 5 items for a rupee. What is the gain

or loss percent?

Solution:

Cost price of the item = 1/6 Rs

SP of the item = 1/5 Rs

Percentage profit = 1/5−1/6

1/6× 100 = 20%

[Ans: 20%]

Example-7 A man buys 12 items for a rupee. How

many items for a rupee should he sell in order to

gain 20%?

Solution:

CP = 1/12

When the gain is 20%, SP = 1.2CP or 120% of CP

SP = 1.2 (1/12) = 1/10 Rs

Number of items sold for a rupee = 1

110⁄

= 10 items

[Ans: 10]

QUESTIONS ON CALCULATING MARKED PRICE ,

SELLING PRICE, DISCOUNT% AND PREMIUM

PERCENTAGE

Example-7 A trader buys an article for Rs 600 and

marks it up by 20%. He then gives a discount of 10%

on the marked price. Find the selling price of the

item

Solution:

CP = Rs 600 ; Mark up % = 20 ; Discount % = 10%

Marked price = CP + 20% of CP or 120% of CP

Marked Price = 600 + 20% of 600. =Rs 720

SP = Marked Price – 10% of Marked Price

or 90% of MP

= 720 – 10% of 720 = Rs 648

[Ans: Rs 648]

Example-8 A trader buys an article for Rs 800 and

marks it up by 25%. He then gives a discount of 5 %

on the marked price. Find the selling price of the

item

Solution:

CP = Rs 800

Marked Price = 800 + 25% of 800 or 125% of 800

Marked Price = Rs 1000

SP = 1000-5% Of 1000 = Rs 950

[Ans: Rs 950]

Example-9 A man buys an item for a discount of

20%. On selling the item for Rs 600, the man earns

a profit of 20%. By what percent is the marked price

of the item higher than the cost price?

Solution:

SP= Rs 500 ; Discount %= 20 ; Profit % = 20

Since there is a 20% profit, therefore

SP = 120% of CP

600 = 120% of CP or CP = Rs 500

Since there is a discount of 20%, we have

SP = MP-20% of MP = 80% of MP

600 = 80% of MP or MP =Rs 750




4

Percentage by which MP is more than CP

=MP−CP

CP× 100 =

750−500

500× 100 = 50%

Method-2

We must recognize that SP can be calculated from

two ways: from CP and from MP

120% of CP = SP = 80% of MP

Or 120% of CP = 80% of MP

MP

CP=

120

80

MP

CP= 1.5

MP = 1.5 CP

which means MP is 50% more than CP

[Ans: 50%]

Example-10 On selling an item for a discount of 30%

a man gains 26%. What is the gain if the discount

percentage is 10%?

Solution:

According to the question, gain is 26% therefore,

If CP = Rs 100

SP = 100+ 26% of 100 = Rs 126

Similarly if discount % = 30%

SP = MP-30% of MP

126 = MP-30% of MP

126 = 70% of MP

MP = Rs 180

Now if the discount percent is 10%, we have

SP= 180-10% of 180 = Rs 162

Gain % = 162−100

100× 100 = 62%

Method-2

SP = 126% of CP=70% of MP

MP

CP=

126

70

MP =1.8CP

On discounting MP by 10% we have

SP = 1.8CP-10% of CP = 1.62CP

SP=1.62CP

Or 62% profit

[Ans: 62%]

Example-11 The cost price of 10 items is equal to

the selling price of 8 items. What is the gain or loss

percent?

Solution:

Method-1

The first method relies on making appropriate

assumptions to solve the above question. We

assume some value for CP of 10 items and SP of 8

items.

Since it is the same number, we will be better of by

assuming some value that is a multiple of both 10

and 8. Therefore taking the LCM of (8, 10) = 40

CP of 10 items = SP of 8 items = Rs 40

CP of 10 items = 40

CP= Rs4

SP of 8 items = Rs 40

SP = Rs 5

Gain % = 5−4

4× 100 = 25%

Method-2

Gain % = SP−CP

CP× 100 =

Gain % = (SP

CP−

𝐶𝑃

𝐶𝑃) × 100

Gain% = (SP

CP− 1) × 100

From the above, we can see that to calculate gain

percentage, we simply require the ratio of SP and

CP

From the information provided in the question we

have

CP of 10 items = SP of 8 items

10 CP= 8SP

SP

CP=

10

8

SP

CP= 1.25

SP= 1.25 CP or SP = 125% of CP

The above equation easily tells us that the profit

percent is 25%

[Ans: 25%]

Example-12 The cost price of 15 items is equal to

the selling price of 20 items. What is the gain or loss

percent?

Solution:

Example-13 On selling 12 items, a man gains selling

price of 2 items. What is the gain percentage of the

man?

Solution:

For the above question, assume the SP to be Rs 10




5

Sale on selling 12 items = 12 x 10 = Rs 120

Profit on selling 12 items = 2 x 10 = Rs 20

Cost = Sale – Profit = 120-20 = Rs 100

Gain percentage = 120−100

100× 100 = 20%

[Ans: 20%]

Example 14. A man sold a horse at a loss of 7%. Had

he been able to sell it at a gain of 9%, it would have

fetched Rs 64 more than it did. What was the cost

price?

Solution: If the cost of the horse = Rs. x

Then, SP at a loss of 7% = 0.93

SP at a gain of 9% = 1.09 x

It is given that

=> 1.09 x – 0.93 x = 64

=> 0.16 x = 64, or x = 400

[Ans: Rs 400]

Example 15. A dealer sold a radio at a loss of 2.5%.

Had he sold it for Rs. 100 more, he would have

gained 7.5%. For what value should he sell it in order

to gain 20 %?

Solution: Let CP of radio be Rs. x

Selling at a loss of 2.5% SP = 97.5% of x = 0.975x.

Also given, (0.975 x + 100) as SP would yield a gain

of 7.5%

But when gain is 7.5%, SP = 107.5% of CP

107.5% of CP = 97.5% of CP + 100

10% of CP = 100

CP= Rs 1000

To gain 20%, the dealer should sell at 120% of CP

SP = 120% of 1000 = Rs 1200

Shortcut Method:

Note that if the radio is sold for Rs 100 more, then

S.P. changes from 97.5% of C.P. to 107.5% of C.P.

Therefore, Rs 100 must amount to a 10% change in

C.P.

10% of C.P. = Rs. 100

C.P. = Rs 1000

For 20 % gain,

S.P. = 120% of 1000= Rs 1200

[Ans: Rs 1200]

Example 16. A person sells an article at a profit of

10%. If he had bought it at 10% less and sold it for

Rs. 3 more, he would have gained 25%. Find the cost

price.

Solution: Let CP be = x; SP = 110% of x = 1.1x

If New CP = 0.9 x and New SP = 1.1 x + 3

then, gain% = 25

Gain % = (1.1x+3)−0.9x

0.9x× 100 =25

0.2x+3 = 0.25 x 0.9x

0.2x+ 3 = 0.225x

0.025x =3

X= Rs 120

[Ans: Rs 120]

Example 17. An article is sold at 20% profit. If its

cost price is increased by Rs 50 and at the same time

if its selling price is also increased by Rs. 30, the

percentage of profit reduces to 8%. Find the cost

price.

Solution: Let the original cost price be Rs. x

Then, original selling price is Rs. 1.2 x

New SP = 1.2x + 30

New CP= x + 50

Gain % = (1.2x+30)−(x+50)

x+50× 100 = 8

0.2x- 20 = 0.08 (x+50)

0.12x = 24

x = Rs 200

[Ans: Rs 200]

Example 18. A sells a bicycle to B at a profit of 30%

and B sells it to C at a loss of 20%. If C pays Rs. 520

for it, at what price did A buy?

Solution: The detailed algebraic method of solving

such problems is as follows:

Let x be C.P. of cycle to A.

Then CP of B = 130% of x = 1.3 x

And CP of C = 80% of (1.3) x = Rs. 520

x = Rs 500

[Ans: Rs 500]

Example 19. If goods be purchased for Rs 840, and

one-fourth be sold at a loss of 20%, at what gain per

cent should the remainder be sold so as to gain 20%

on the whole transaction?

Solution: Total Cost of goods = Rs. 840

Cost of one fourth of the goods = Rs 210




6

S.P. of one fourth = 0.8 x (210) = 168

Gain desired = 20%

Total Revenue = 1.2 x (840) = 1008

Additional Revenue = 1008 – 168 = Rs. 840

Cost of remaining goods = 840 – 210 = Rs. 630

Since Rs. 840 have to be realized by selling goods

which cost Rs. 630.

% Profit = 840−630

630× 100 = 33

1

3 %

[Ans: Rs 𝟑𝟑𝟏

𝟑 % ]

Example 20. A man purchases 5 horses and 10 cows

for Rs 10000. He sells the horses at 15% profit and

the cows at 10% loss. Thus, he gets Rs. 375 as profit.

Find the cost of 1 horse and 1 cow separately.

Solution: Let Rs. x be the cost of one horse

Then, 5x will be the cost of 5 horses and

Rs. (10000 – 5x) cost of 10 cows.

Total profit = Profit on horses + Profit on cows

=> 375 = 0.15 (5x) -0.1(10000-5x)

=> 375 = 0.75x – 1000 + 0.50x

=> 1375 = 1.25x

=> x = Rs. 1100

Cost of 10 cows = 10000 – 5500 = Rs 4500

Cost of 1 cow = Rs 450

[Ans: Rs 1100, Rs 450]

Example 21. A dishonest dealer professes to sell his

goods at cost price, but he uses a weight of 950 gm

for the kg weight. Find his gain percent.

Solution:

In such questions, the trader uses a faulty weight to

weigh goods while selling. But when the trader or

the dealer buys goods, the correct weight is used.

Thus, is the trader is using a weight of 950g instead

of a kg weight the following should happen:

- While selling he will charge for 1 kg but will give

away only 950 g of goods

- While buying he will buy only 950g of goods and

will pay for only 950g of goods.

Assume that the cost price = Re 1 per gram

Total cost of the trader to buy 950g = Rs 950

While selling, though he claims to sell at cost price,

he claims to sell 1000 g despite giving away only

950g worth of material.

Therefore,

SP = Re 1 per gram = CP

Sale for 1000g = Rs 1000

gain % = 1000−950

950× 100 = 5

5

19 % gain

[Ans: 55

19 % ]

Example 22. A dishonest dealer sells goods at a loss

of 5%. But instead of 1 kg he uses a weight of 900

gm while selling. Find his percentage gain.

Solution:

The trader uses a faulty weight to weigh goods

while selling. But when the trader or the dealer buys

goods, the correct weight is used.

Thus, is the trader is using a weight of 900g instead

of a kg weight the following should happen:

- While selling he will charge for 1 kg but will give

away only 900 g of goods

- While buying he will buy only 900g of goods and

will pay for only 900g of goods.

Assume CP = Re1 per gram;

SP = 1- 5% of 1 = 0.95 per gram

The cost of the trader = 1 x 900 = Rs 900

The sale of the trader = 0.95 x 1000 = Rs 950

gain % = 950−900

900× 100 = 5

5

9 % gain

[Ans: 55

9 % ]

Example 23. Nandlal purchased 20 dozen notebooks

at Rs 48 per dozen. He sold 8 dozen at 10% profit

and the remaining 12 dozen at 20% profit. What is

his profit percentage in this transaction ?

Solution: Total investment on buying 20 dozen

notebooks = 20 x 48 = Rs. 960

Sales is in two parts:

Sales 1 @ 10% profit: 8(1.1)48 = 422.4

Sales 2 @ 20% profit: 12(1.2)48 = 691.2

Net sales = 422.4 + 691.2 = Rs 1113.6

gain % = 1113.6−960

960× 100 = 16% gain

[Ans: 16 % ]




7

Example 24. A man purchased a certain number of

mangoes at 3 per rupee and the same number at 4

per rupee. He mixes them together and sells them at

3 per rupee. What is his gain or loss percent?

Solution: Let x be the number of mangoes

purchased at each of the given rates

First type of mangoes he bought at 3 per rupee

CP of one mango = = 1

3

CP of x mangoes = = x

3

Then, total cost of purchase

= x

3+

x

4=

7x

12

SP of each mango = 1

3

Sale on selling 2x mangoes = 2x

3

gain % = 2x

3−

7x

127x

12

× 100

gain % = x

7x× 100 = 14

2

7 %

Method-2

To solve questions where the number of mangoes

bought of each kind is the same, we need to assume

a number such that the purchase price of each type

must be an integer.

For example, suppose the man purchased a

multiple of 3, he will get an integer value for the

total purchase price of the first type of mangoes.

Similarly, if he purchases a number of mangoes that

is a multiple of 4, he will get an integer value of the

total cost of the 2nd type of mangoes.

To get an integer value for the cost of both types of

mangoes, we must assume that he buys a number

of mangoes that is a common multiple of 3 and 4.

The LCM of 3 and 4 = 12

Assume that the man buys 12 mangoes of each type

Cost of purchase of the first type of mangoes = 12/3

= Rs 4

Cost of the purchase of the 2nd type of mangoes =

12/4 = Rs 3

Total cost of purchase = Rs 7

SP of one mango = 1/3

Total sale on selling 24 mangoes = 24/3 = Rs 8

Profit % = 8−7

7× 100 = 14

2

7 %

[Ans: 𝟏𝟒𝟐

𝟕 %]

Example 25. A trader allows a discount of 5% for

cash payment. How much % above cost price must

he mark his goods to make a profit of 10% ?

Solution: Assume that the C.P. = Rs 100

S.P. for 10% profit = Rs 110.

M.P. must be such that on giving a discount of 5%

of the M.P., he sells the item at Rs 110

95% of M.P. = Rs. 110

M.P. = 110

95× 100 =

2200

19= 115

15

19 Rs.

The % by which M.P. is greater than C.P.

=115

15

19−100

100 × 100 = 15

15

19 %

[Ans: 𝟏𝟓𝟏𝟓

𝟏𝟗 %]

Example 26. A horse worth Rs 9000 is sold by A to

B at 10% loss. B sells the horse back to A at 10% gain.

What is the gain of B ?.

Solution:

Initial CP of A = Rs 9000

SP of A= CP of B= 90% of 9000= Rs 8100

SP of B= CP of A = 110% OF 8100 = Rs 8910

Gain of B = SP of B- CP of B= 8910 -8100= Rs 810

[Ans: 𝐑𝐬 𝟖𝟏𝟎

Example 27. A man sells two horses for Rs 1710. The

cost price of the first is equal to the selling price of

the second. If the first is sold at 10% loss and the

second at 25% gain, what is his total gain or loss (in

rupees)

Solution:

CP of the first horse = x

SP of the 2nd horse = x

SP of the first horse = 1710-x

Loss on the sale of the first horse = 10%, therefore

90% of x = 1710-x

1.9x = 1710

x = 900 = CP of the first horse and SP of 2nd

The 2nd horse is sold at a gain of 25% therefore

900 = 125% of y

Y= CP of the 2nd horse

y =720

Total cost = 900 + 720 = Rs 1620




8

Total sale = Rs 1710

Net gain = 1710 – 1620 = Rs 90

[Ans: Rs 90]

Example 28. If a dishonest shopkeeper measures 4

cm less of a metre then find how much percent he

earns by this way.

Solution:

First, let us understand what this question implies.

When the shopkeeper sells, he measures 4cm less

than a metre but charges money for one metre.

Thus the following two things are meant by the

above question

- The shopkeepers cost is 96 cm of cloth

-The shopkeepers revenue is 100 cm of cloth.

Assuming that his CP and SP are the same. = Re 1

per cm of cloth

Cost of the trader = Rs 96

Sale of the trader = Rs 100

Profit% = 100−96

96× 100 = 4

1

6 %

[Ans: 41

6 %]

EXERCISE-1

1. A dealer buys at the rate of 100 wristwatches for Rs 5060 and sells at the rate of 110 watches for Rs 5060 In this business his loss% was

(a) 111

9% (b) 33

1

3%

(c) 162

3 % (d) 9

1

11

2. A motor – cycle is sold at a gain of 18%. if it had been

sold for Rs 490 more then , 23% would have been gained . The cost price of the motor – cycle is

(a) Rs. 10500 (b)Rs 9500 (c) Rs 9800 (d) Rs 12000 3. A man sells two houses at the rate of Rs 1995 lakh

each. On one of the gains 5% and on other he loses 5% his gain or loss percent in the whole transaction is

(a) 0.25% loss (b) 0.25% gain (c) 2.5% loss (d) neither loss, nor gain 4. Successive discount of 30% and 10% are equivalent

to a single discount of (a) 30% (b) 40% (c) 37% (d) 45% 5. By selling an article for Rs. 69, there is a loss of 8%.

When the article is sold for Rs. 78 the gain or loss percent is

(a) neither loss nor gain (b) 4% gain (c) 4% loss

(d) 40% gain 6. Profit after selling an article for Rs. 425 is the same

as the loss after selling it for Rs 355. The cost of the article is

(a) Rs. 385 (b) Rs .390 (c) 395 (d) 400 7. If I had purchased 11 articles for Rs. 10 and sold all

the articles at the rate of 10 for Rs. 11, the Profit percent would have been (a) 10% (b) 11% (c) 21% (d) 100% 8. If a merchant estimates his profits as 20% of the

selling price, what is his real profit percent? (a) 20% (b) 22% (c) 25% (d) 30% 9. A stockists wants to make some profit in selling

sugar. He contemplates about various methods.

Which of the following would maximise his profit?

I. Sell sugar at 10% profit

II. Use 900 gm of weight instead of 1 kg and sell at

CP

III. Mix 10% impurities in sugar and sell at CP




9

IV. Increase the price by 5% and reduce weights by

5%

(a) IV (b) II

(c) I (d) II or IV

10. A company sells it colour TVs in market at Rs 8400.

Of this 30% are the manufacturing costs, 25%

marketing costs and 15% administration expenses,

rest is profit. Next year, if the manufacturing

expenses go up by 20%, marketing expenses by 10%,

and the company increases the selling price by 10%,

what will be the percentage increase/decrease in

profit?

(a) 0% (b) 10%

(c) 7% (d) 5%

11. If (Cost Price/Selling Price) × 100 = 75, what percent

of cost price is profit?

(a) 25% (b) 33 1

3 %

(c) 40% (d) None of these

12. An article is sold at a profit of 20%. If both the cost

price and selling price are Rs 100 less, the profit will

be 4% more. Find the cost price.

(a) Rs 600 (b) Rs 400

(c) Rs 460 (d) Rs 480

13. A shopkeeper claims to sell milk at 9 1

11 % loss, but

he adulterates milk with water. In what ratio does he

mix milk with water to gain 16 2

3 %

(a) 17 : 60 (b) 17 : 77

(c) 60 : 17 (d) 54 : 39

14. A person purchases 80 clocks and sells 30 at a gain

of 10% and 50 at a gain of 20%. Had he sold all of

them at a uniform profit of 15%, he would have got

Rs 400 less on total sales. Find the cost price of each

clocka

(a) Rs 400 (b) Rs 333.33

(c) Rs 420 (d) Rs 560

15. A manufacturer of a certain item can sell all he can

produce at the selling price of Rs. 60 each. It costs

him Rs. 40 in materials and labour to produce each

item and he has overhead expenses of Rs. 3000 per

week in order to operate that plant. The number of

units he should produce and sell in order to make a

profit of at least Rs. 1000 per week is

(a) 400 (b) 300

(c) 250 (d) 200

16. A shopkeeper sold an article for Rs. 6,750 after

giving a discount of 10% on the labelled price. He

would have earned a profit of 50%, had there been no

discount. What was the actual percentage of profit

earned ?

(a) 36 (b) 40

(c) 35 (d) None of these

17. A house costs C rupees. Later it was sold for a profit

of 25%. What is the capital gains tax if it is 50% of

the profit?

(a) C/24 (b) C/8

(c) C/4 (d) C/2

18. If selling price is doubled, the profit triples. Find the

profit percent.

(a) 66 2

3 (b) 100

(c) 105 1

3 (d) 120

19. A showroom owner sells a leather jacket for Rs. X

and claims to make a profit of 10%. He plans to have

a stall in the trade fair and marks the same jacket at

Rs. 2X. At the stall, he allows a discount of 20%.

What will be the percentage profit that he will make

at the trade fair ?

(a) 80% (b) 60%

(c) 76% (d) None of these

20. A shopkeeper sells wheat at a profit of 10% and uses

weights which are 20% less than the actual weight.

The total gain earned by him will be

(a) 30% (b) 88%

(c) 37.5% (d) None of these




10

Answer Key

1( d) 2(c) 3(a) 4(c)

5(b) 6(b) 7(c) 8(c)

9(b) 10(d) 11(b) 12(b)

13(c) 14(a) 15(d) 16(c)

17(c) 18(b) 19(c) 20(c)


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