Exercise :: 5


1. A man sells an article at 5% profit. If he had bought it at 5% less and sold it for 1 less, he would have gained 10%. The cost price of the article is :
(a) 200
(b) 150
(c) 240
(d) 280
(e) None of these
Ans.a

Let the CP of the article be x.

Then, SP = 105x100

Now, new CP = 95x100 and new SP = 105x100 - 1

According to the question

\(\frac{105x}{100} - 1 - \frac{95}{100} = \frac{10 \times 95x}{100 \times 100}\)

∴ x = 200

2. Five kg of butter was bought by a shopkeeper for 300. One kg becomes unsaleable. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg was the butter sold?
(a) 67.50
(b) 52.50
(c) 60
(d) 72.50
(e) None of these
Ans.a

Let S.P. = x per kg

∴ S.P. of 4 kg = 4x

∴ 4x = \(\frac{100 - 40}{100} \times 300\)

⇒ x = 2704 = 67.50

3. A fruit seller sells 8 oranges at a cost price of 9. The profit per cent is
(a) 1212
(b) 1119
(c) 51517
(d) 823
(e) None of these
Ans.a

Let C.P. of one orange = 1

Then C.P. of 8 oranges = 8

S.P of 8 oranges = 9

∴ Gain % = \(\frac{9 - 8}{8} \times 100 = \frac{100}{8} = 12\tfrac{1}{2} \%\)

4. The cost price of 20 articles is equal to the selling price of 25 articles. The loss percent in the transaction is
(a) 5
(b) 20
(c) 25
(d) 30
(e) None of these
Ans.c

Let C.P. of 1 article = 1

then C.P. of 25 articles = 25

and S.P. of 25 articles = 20

∴ loss % = \(\frac{25 - 20}{20} \times 100 = 25\%\)

5. By selling 66 metres of cloth a person gains the cost price of 22 metres. Find the gain per cent.
(a) 22%
(b) 2212%
(c) 33%
(d) 3313%
(e) None of these
Ans.d

Let C.P. of one metre of cloth = 1

then C.P. of 66 metres of cloth = 66

Gain = C.P. of 22 metres = 22

% gain = 2266 × 100 = 3313%

Shortcut method :

If on selling ‘x’ articles, a man gains equal to the C.P. of ‘y’ articles, then % gain = yx × 100

∴ % gain = = 2266 × 100 = 3313%

6. By selling 66 metres of cloth a man loses the selling price of 22 metres. Find the loss per cent.
(a) 20%
(b) 25%
(c) 30%
(d) 35%
(e) None of these
Ans.b

Loss = C.P. of 66 metres – S.P. of 66 metres

= S.P. of 22 metres

⇒ C.P. of 66 metres = S.P. of 88 metres

% loss = \(\frac{loss}{C.P. \; of \; 66 \; metres} \times 100\)

= \(\frac{S.P. \; of \; 22 \; metres}{C.P. \; of \; 66 \; metres} \times 100\)

= \(\frac{S.P. \; of \; 22 \; metres}{S.P. \; of \; 88 \; metres} \times 100\)

= 2288 × 100 = 25%

* Try to solve by shortcut method

7. A single discount equal to a discount series of 10% and 20% is
(a) 25%
(b) 28%
(c) 30%
(d) 35%
(e) None of these
Ans.b

Equivalent discount = 10 + 20 - \(\frac{10 \times 20}{100}\)

= 30 – 2 = 28%

8. The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate?
(a) 12%
(b) 14%
(c) 15%
(d) 18%
(e) None of these
Ans.c

Retailer price = list price \(\left ( 1 - \frac{d_{1}}{100} \right )\left ( 1 - \frac{d_{2}}{100} \right )\)

⇒ 122.40 = 160\(\left ( 1 - \frac{10}{100} \right )\left ( 1 - \frac{d_{2}}{100} \right )\)

\(1 - \frac{d_{2}}{100} = \frac{122.40 \times 100}{160 \times 90} = 0.85\)

⇒ d2 = (1 - 0.85) × 100 = 15%

9. A tradesman is marketing his goods 20% above the cost price of the goods. He gives 10% discount on cash payment, find his gain percent.
(a) 12%
(b) 8%
(c) 15%
(d) 18%
(e) None of these
Ans.b

Let the C.P. of the goods be 100

⇒ Marked price of the goods = 120

Discount = 10% ⇒ S.P. is 90% of 120 = 108

∴ Gain = (108 – 100) i.e. 8%.

10. For a certain article, if discount is 25%, the profit is 25%. If the discount is 10%, then the profit is
(a) 10%
(b) 20%
(c) 35%
(d) 50%
(e) None of these
Ans.d

For same article, \(\frac{100 - d_{1}}{100 - d_{2}} = \frac{100 + g_{1}}{100 + g_{2}}\)

\(\frac{100 - 25}{100 - 10} = \frac{100 + 25}{100 + g_{2}} \Rightarrow \frac{75}{90} = \frac{125}{100 + g_{2}}\)

⇒ 100 + g2 = \(\frac{90 \times 125}{75} = 150\) ⇒ g2 = 50%

11. A trader marks his goods at such a price that he can deduct 15% for cash and yet make 20% profit. Find the marked price of an item which costs him 90 :
(a) 1351113
(b) 105321
(c) 127117
(d) 95121
(e) None of these
Ans.c

SP = 90 × 1.2 = 108

Marked price = 1080.85 = 127.05

12. A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should be his rate of mark up on an article costing 9?
(a) 20%
(b) 6623%
(c) 30%
(d) 1003%
(e) None of these
Ans.d

Let the SP of the article be x

Expenses = 15% of x = 0.15x

Profit = 10% of x = 0.10x

CP = 9 (given)

Therefore, 9 + 0.15x + 0.1x = x ⇒ x = 12

∴ % increase for marked price = \(\frac{12 - 9}{9} \times 100 = \frac{100}{3} \%\)