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Profit And Loss Questions

Profit and Loss – Important Formulas

IMPORTANT FACTS

Cost Price:

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

Selling Price:

The price, at which an article is sold, is called its selling prices, abbreviated as S.P.

Profit or Gain:

If S.P. is greater than C.P., the seller is said to have a profit or gain.

Loss:

If S.P. is less than C.P., the seller is said to have incurred a loss.

IMPORTANT FORMULAE

Gain = (S.P.) – (C.P.)

Loss = (C.P.) – (S.P.)

Loss or gain is always reckoned on C.P.

Gain % =

x 100

C.P.

Loss % =

x 100

C.P.

Selling Price: (S.P.)

SP =

(100 + Gain %)

x C.P

100

Selling Price: (S.P.)

SP =

(100 – Loss %)

x C.P.

100

Cost Price: (C.P.)

C.P. =

100

x S.P.

(100 + Gain %)

Cost Price: (C.P.)

C.P. =

100

x S.P.

(100 – Loss %)

If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.

If an article is sold at a loss of say, 35% then S.P. = 65% of C.P.

When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:

Loss % =

Common Loss and Gain %

2

=

x

2

.

10

10

If a trader professes to sell his goods at cost price but uses false weights, then

Gain % =

Error

x 100

%.

(True Value) – (Error)

Profit and Loss – General Questions

1.

Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

A.

15

B.

16

C.

18

D.

25

Answer: Option B

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 – x).

20 – x

x 100 = 25

x

2000 – 100x = 25x

125x = 2000

x = 16.

3.

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

A.

66

2

3

B.

100

C.

105

1

3

D.

120

Answer: Option B

Explanation:

Let C.P. be Rs. x and S.P. be Rs. y.

Then, 3(y – x) = (2y – x) y = 2x.

Profit = Rs. (y – x) = Rs. (2x – x) = Rs. x.

Profit % =

x

x 100

% = 100%

x

4.

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A.

3

B.

4

C.

5

D.

6

Answer: Option C

Explanation:

C.P. of 6 toffees = Re. 1

S.P. of 6 toffees = 120% of Re. 1 = Rs.

6

5

For Rs.

6

, toffees sold = 6.

5

For Re. 1, toffees sold =

6 x

5

= 5.

6.

The percentage of profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make a 25% profit?

A.

Rs. 2000

B.

Rs. 2200

C.

Rs. 2400

D.

Data inadequate

Answer: Option A

Explanation:

Let C.P. be Rs. x.

Then,

1920 – x

x 100 =

x – 1280

x 100

x

x

1920 – x = x – 1280

2x = 3200

x = 1600

Required S.P. = 125% of Rs. 1600 = Rs.

125

x 1600

= Rs 2000.

100

7.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

A.

Rs. 18.20

B.

Rs. 70

C.

Rs. 72

D.

Rs. 88.25

Answer: Option C

Explanation:

C.P. = Rs.

100

x 392

= Rs.

1000

x 392

= Rs. 320

122.5

1225

Profit = Rs. (392 – 320) = Rs. 72.

8.

A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

A.

Rs. 1090

B.

Rs. 1160

C.

Rs. 1190

D.

Rs. 1202

Answer: Option C

Explanation:

S.P. = 85% of Rs. 1400 = Rs.

85

x 1400

= Rs. 1190

100

9.

Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

A.

3.5

B.

4.5

C.

5.6

D.

6.5

Answer: Option C

Explanation:

Cost Price of 1 toy = Rs.

375

= Rs. 31.25

12

Selling Price of 1 toy = Rs. 33

So, Gain = Rs. (33 – 31.25) = Rs. 1.75

Profit % =

1.75

x 100

%

=

28

% = 5.6%

31.25

5

10.

Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. The gain percent is:

A.

30%

B.

33

1

%

3

C.

35%

D.

44%

Answer: Option D

Explanation:

Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.

C.P. of 30 articles = Rs.

5

x 30

= Rs. 25.

6

S.P. of 30 articles = Rs.

6

x 30

= Rs. 36.

5

Gain % =

11

x 100

% = 44%.

25

Question Answer

1. 1043 को किसी संख्या से भाग देने पर भागफल 11 तथा शेषफल 20 प्राप्त होता है, भाजक ज्ञात कीजिए ?

(A) 95

(B) 93

(C) 73

(D) 97

(B) 93

2. किसी संख्या को 195 से भाग देने पर 47 शेष बचते हैं, इस संख्या को 15 से भाग देने पर शेष क्या बचेगा ?

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