ICSE Class 9 Maths Chapter 02 Profit Loss and Discount

Profit, Loss And Discount

Exercise 2 (A)

Question 1

Find the profit or loss percent, when:

(i) C.P. = Rs. 55 and S.P. = Rs. 72.60

(ii) C.P. = Rs. 490 and S.P. = Rs. 416.50

(iii) C.P. = Rs. 112, overheads = Rs. 14 and S.P. = Rs. 94.50.

Solution (i)

C.P. = Rs. 55

S.P. = Rs. 72.60

Gain = S.P. - C.P. = Rs. 72.60 - Rs. 55.00 = Rs. 17.60

Gain percent = \(\frac{\text{Gain} \times 100}{\text{C.P.}}\)

= \(\frac{17.60 \times 100}{55}\) %

= \(\frac{1760 \times 100}{100 \times 55}\) % = 32 %

Solution (ii)

C.P. = Rs. 490

S.P. = Rs. 416.50

Loss = C.P. - S.P. = Rs. 490.00 - 416.50 = Rs. 73.50

Loss % = \(\frac{\text{Loss} \times 100}{\text{C.P.}}\) = \(\frac{73.50 \times 100}{490}\) %

= \(\frac{7350 \times 100}{100 \times 490}\) % = 15%

Solution (iii)

C.P. = Rs. 112

Overheads = Rs. 14

Total C.P. = Rs. 112 + Rs. 14 = Rs. 126

S.P. = Rs. 94.50

Loss = C.P. - S.P. = Rs. 126 - Rs. 94.50 = Rs. 31.50

Loss % = \(\frac{\text{Loss} \times 100}{\text{C.P.}}\) = \(\frac{31.50 \times 100}{126}\) %

= \(\frac{3150 \times 100}{100 \times 126}\) % = 25% Ans.

Teacher's Note

Understanding profit and loss helps in everyday shopping and business transactions, allowing us to make informed decisions about purchases and pricing.

Question 2

Find S.P. when:

(i) C.P. = Rs. 435 and loss = 16%

(ii) C.P. = Rs. 172, overheads = Rs. 61 and gain = 12%.

Solution (i)

C.P. = Rs. 435, Loss = 16%

S.P. = \(\frac{\text{C.P.} \times (100 - \text{Loss} \%)}{100}\)

= \(\frac{435 (100 - 16)}{100}\) = \(\frac{435 \times 84}{100}\)

= Rs. 365.40.

Solution (ii)

C.P. = Rs. 172

Overheads = Rs. 61

Total C.P. = Rs. 172 + Rs. 61 = Rs. 233

Gain = 12%

S.P. = \(\frac{\text{C.P.}(100 + \text{gain} \%)}{100}\)

= \(\frac{233(100 + 12)}{100}\) = \(\frac{233 \times 112}{100}\)

= Rs. 260.96 Ans.

Question 3

Find C.P. when:

(i) a cycle is sold for Rs. 1485 at a profit of 8%.

(ii) a fan is sold for Rs. 657.60 at a loss of 4%.

Solution (i)

S.P. of cycle = Rs. 1485

Profit = 8%

C.P. = \(\frac{\text{S.P.} \times 100}{100 + \text{gain} \%}\) = \(\frac{1485 \times 100}{100 + 8}\)

= Rs. \(\frac{1485 \times 100}{108}\) = Rs. 1375.

Gain = S.P. - C.P. = Rs. 188.60 - Rs. 164 = Rs. 24.60

Gain % = \(\frac{\text{Gain} \times 100}{\text{C.P}}\) = \(\frac{24.60 \times 100}{164}\) = \(\frac{2460 \times 100}{100 \times 164}\) % = 15%. Ans.

Question 4

If oranges are bought at 11 for Rs. 30 and sold at 10 for Rs. 31, find loss or gain percent.

Solution

L.C.M. of 11 and 10 = 110

C.P. of 110 oranges = \(\frac{110 \times 30}{11}\) = Rs. 300

S.P. of 110 oranges = \(\frac{110 \times 31}{10}\) = Rs. 341

Gain = S.P. - C.P. = Rs. 341 - Rs. 300 = Rs. 41 Ans.

Gain % = \(\frac{\text{Gain} \times 100}{\text{C.P.}}\) = \(\frac{41 \times 100}{300}\) % = \(\frac{41}{3}\) % = 13\(\frac{2}{3}\) % Ans.

Question 5

By selling an article for Rs. 123, the shopkeeper loses 25%. Find the gain or loss percent, if the article be sold for Rs. 188.60.

Solution

In first case, S.P. = Rs. 123

Loss = 25%

C.P. = \(\frac{\text{S.P.} \times 100}{100 - \text{Loss} \%}\) = \(\frac{123 \times 100}{100 - 25}\)

= \(\frac{123 \times 100}{75}\) = Rs. 164

In second case,

S.P. = Rs. 188.60

C.P. = Rs. 164

Teacher's Note

When shopping during sales, calculating the actual profit or loss helps us understand whether we are getting a genuine discount or being misled by artificially inflated original prices.

Question 6

A dealer sold two almirahs for Rs. 6090 each gaining 16% on one and losing 16% on the other. Find his net gain or loss percent in the whole transaction.

Solution

S.P. of first almirah = Rs. 6090

Gain % = 16%

C.P. = \(\frac{\text{S.P.} \times 100}{100 + \text{Gain} \%}\) = \(\frac{6090 \times 100}{100 + 16}\)

= Rs. \(\frac{6090 \times 100}{116}\) = Rs. 5250

S.P. of the second almirah = Rs. 6090

Loss = 16%

C.P. = \(\frac{\text{S.P.} \times 100}{100 - \text{Loss} \%}\) = \(\frac{6090 \times 100}{100 - 16}\)

= Rs. \(\frac{6090 \times 100}{84}\) = Rs. 7250

Total C.P. of both almirahs = Rs. 5250 + 7250 = Rs. 12500

and total S.P. = Rs. 6090 + Rs. 6090 = Rs. 12180

Loss = C.P. - S.P. = Rs. 12500 - 12180 = Rs. 320

Loss % = \(\frac{\text{Loss} \times 100}{\text{C.P.}}\) = \(\frac{320 \times 100}{12500}\) % = 2.56% Ans.

Question 7

By selling a book for Rs. 115.20, a man loses 10%. At what price should he sell it to gain 5%?

Solution

S.P. of book = Rs. 115.20

Loss = 10%

C.P. = \(\frac{\text{S.P.} \times 100}{100 - \text{Loss} \%}\) = \(\frac{115.20 \times 100}{100 - 10}\)

= \(\frac{11520 \times 100}{100 \times 90}\) = Rs. 128

If gain = 5%

then S.P. = \(\frac{\text{C.P.}(100 + \text{gain} \%)}{100}\)

= \(\frac{128 (100 + 5)}{100}\) = Rs. \(\frac{128 \times 105}{100}\)

= Rs. 134.40 Ans.

Question 8

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs. 10.50 less, he would have gained 30%. Find the cost price of the article.

Solution

Let C.P. of an article = Rs. 100

Gain = 25%

S.P. = Rs. 100 + 25 = Rs. 125

In second case C.P. = Rs. 100 - 20 = Rs. 80

Gain = 30%

S.P. = \(\frac{\text{C.P.}(100 + \text{Gain} \%)}{100}\)

= Rs. \(\frac{80 \times (100 + 30)}{100}\) = Rs. \(\frac{80 \times 130}{100}\)

= Rs. 104

Difference between two S.P.'s = Rs. 125 - 104 = Rs. 21

If difference is Rs. 21, then C.P. = Rs. 100 and if difference is Rs. 10.50, then

C.P. = Rs. \(\frac{100 \times 10.50}{21}\)

= Rs. \(\frac{100 \times 1050}{100 \times 21}\) = Rs. 50 Ans.

Question 9

20% more can be gained if a piece of cloth is sold for Rs. 83 instead of Rs. 78. Find the cost price of the piece of cloth.

Solution

Difference in both S.P.'s = Rs. 83 - Rs. 78 = Rs. 5

But difference in gain = 20%

If Rs. 20 is more then C.P. = Rs. 100 and if Rs. 5 is more, then C.P. = Rs. \(\frac{100 \times 5}{20}\) = Rs. 25 Ans.

Question 10

The difference between selling an article at 7% profit and at 16% profit is Rs. 63. Find the cost price of the article and also the two selling prices.

Solution

Difference in percent profit = 16% - 7% = 9%

9% of C.P. = Rs. 63

C.P. = \(\frac{63 \times 100}{9}\) = Rs. 700

Now first S.P. when gain is 7%

= \(\frac{\text{C.P.}(100 + \text{Gain} \%)}{100}\)

= \(\frac{700 (100 + 7)}{100}\)

= Rs. \(\frac{700 \times 107}{100}\) = Rs. 749

Similarly second S.P. when gain is 16%

= \(\frac{700 (100 + 16)}{100}\) = \(\frac{700 \times 116}{100}\)

= Rs. 812 Ans.

Question 11

A man sells an article at 5% above its cost price. If he had bought it at 5% less than what he paid for it and sold it Rs. 2 less, he would have gained 10%. Find the cost price of the article.

Solution

Let C.P. of the article = Rs. 100

First S.P. = Rs. 100 + 5 = Rs. 105

Second time C.P. = 100 - 5 = Rs. 95

Gain = 10%

S.P. = \(\frac{95 \times (100 + 10)}{100}\) = \(\frac{95 \times 110}{100}\)

= Rs. \(\frac{209}{2}\)

Teacher's Note

Profit and loss calculations are fundamental in small business operations, helping shopkeepers determine fair pricing and manage their inventory effectively.

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