Exercise :: 3


1. What per cent of selling price would be 34% of cost price if gross profit is 26% of the selling price?
(a) 17.16
(b) 74.00
(c) 25.16
(d) 88.40
(e) None of these
Ans.c

Let the selling price of the article be 100.

∴ Profit = 26

∴ Cost price of the article = 100 – 26 = 74

∴ Reqd.% = \(\frac{34 \times 74}{100} = 25.16 \%\)

2. A man sold 10 eggs for 5 rupees and gained 20%. How many eggs did he buy for 5 rupees?
(a) 10 eggs
(b) 12 eggs
(c) 14 eggs
(d) 16 eggs
(e) None of these
Ans.b

S.P. for 1 egg = 510 = 12

∴ C.P. for 1 egg = \(\frac{100}{\left (100 + 20 \right )} \times \frac{1}{2} = \frac{5}{12}\)

⇒ He bought 12 eggs for 5 rupees.

3. A person sells 36 oranges per rupee and suffers a loss of 4%. Find how many oranges per rupee to be sold to have again of 8%?
(a) 30
(b) 31
(c) 32
(d) 33
(e) None of these
Ans.c

136 : (100 - 4) :: x : (100 + 8)

⇒ x = \(\frac{108}{96 \times 36} = \frac{1}{32}\)

He sells 32 oranges per rupee.

4. Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made?
(a) 500
(b) 1000
(c) 1500
(d) 2000
(e) None of these
Ans.b

C.P. for one coconut = 150100 = 32

S.P. for one coconut = 2

Profit on one coconut = 2 - 32 = 12

∴ Profit on 2000 coconut = 12 × 2000 = 1000

5. A shopkeeper’s price is 50% above the cost price. If he allows his customer a discount of 30% what profit does he make?
(a) 5%
(b) 10%
(c) 15%
(d) 20%
(e) None of these
Ans.a

Let C.P. = 100, then M. P. = 150

S.P. = 70% of 150 = 105

∴ % profit = \(\frac{105 - 100}{100} \times 100 = 5\%\)

6. A shopkeeper purchases 10 kg of rice at 600 and sells at a loss as much the selling price of 2 kg of rice. Find the sale rate of rice/ kg.
(a) 60 per kg
(b) 50 per kg
(c) 80 per kg
(d) 70 per kg
(e) None of these
Ans.b

Let S. P. = x per kg

∴ S.P. of 2 kg of rice = 2x = Loss

Now, Loss = C.P. – S.P.

2x = 600 – 10x

⇒ x = 50 per kg

7. If 15 oranges are bought for a rupee, how many must be sold for a rupee to gain 25%?
(a) 12
(b) 10
(c) 20
(d) 18
(e) None of these
Ans.a

C.P. for one orange = 115

Then S.P. = \(\frac{100 + 25}{100} \times \frac{1}{15} = \frac{125}{100 \times 15} = \frac{1}{12}\)

Hence S.P. for one orange = 112

∴ 12 oranges must be sold for a rupee

8. A man buys milk at 6 per litre and adds one third of water to it and sells mixture at 7.20 per litre. The gain is
(a) 40%
(b) 80%
(c) 60%
(d) 25%
(e) None of these
Ans.b

C.P. of one litre = 6

After adding water to it One has to pay 7.20 for 23 litre of milk.

So S.P. of 23 litre of milk = 7.20

⇒ S.P. of 1 litre of milk = \(\frac{7.20 \times 3}{2} = 10.80\)

∵ S.P. > C.P.

Hence gain = \(\frac{10.80 - 6}{6} \times 100 = \frac{4.80}{6} \times 100\)

= 0.80 × 100 = 80%

9. A milk man makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?
(a) 30
(b) 403
(c) 22
(d) 10
(e) None of these
Ans.b

Let profit per litre = 20

So, C.P. /litre = 100

S.P. / litre = 120

On adding 10% water to the milk

C.P. / 910 litre = 100

S.P. / 910 litre = 120

S.P / litre = \(\frac{120 \times 10}{9} = \frac{400}{3}\)

⇒ Profit / litre = 4003 - 100 = 33.33

% by which profit increases = 33.33 – 20 = 13.3

10. A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 16%?
(a) 17 per kg
(b) 17.40 per kg
(c) 16.5 per kg
(d) 16 per kg
(e) None of these
Ans.b

C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)

= 3000.

S.P. = 116% of 3000 = (116100 × 3000) = 3480

∴ Rate of S.P. of the mixture = (3480200) per kg

= 17.40 per kg.