Question 1

Find the quantity of rice @ Rs. 10 per kg. which should be mixed with 25 kgs of rice @ Rs. 8 per kg, so that on selling the mixture @ Rs. 15 per kg there is 80% profit.

Accepted Answer

Cost price of the mixture = 15 × (100 / 180) = Rs. 25/3 per kg (Quantity of rice @ Rs. 8 per kg) / (Quantity of rice @ Rs.10 per kg) = (5 / 3) / (1/3) = 1/5 Quantity of rice @ Rs. 10 per kg = 25 × (1/ 5) = 5 kgs.

Question 2

A person has two solutions of sugar with 30% and 50% concentration respectively. In what proportion should he mix two solutions to get 45% concentration in the resulting mixture?

Accepted Answer

He should mix 30% and 50% in the ratio 5 : 15 or 1 : 3. ( 30% Solution ) / (50% Solution) = 1 / 3 or 1 : 3

Question 3

A merchant has 160 kgs of wheat. He sells a part of it at 10% profit and the rest of 6% loss. If he incurs 4% loss on the whole, find the quantity for each part.

Accepted Answer

According to figure we can find that the ration would be 1 : 7. Quantity sold at 10% profit = 1 / (1 + 7)× 160 = 20 kgs. Quantity sold at 6% loss = (160 – 20) = 140 kgs.

Question 4

A man bought a certain quantity of sugar for Rs. 8000. He sells one-fourth of it at 20% loss. At what per cent profit should he sell the remainder stock so as to make an overall profit of 20%?

Accepted Answer

Let the remainder stock be sold at P% profit. (P - 20) / 30 = ((1 / 4) / (3 / 4)) or (P – 20) = 30 × (1 / 3) or P = 20 + 10 P = 30% profit.

Question 5

A person has Rs. 5000. He invests a part of it at 3% per annum and the remainder at 8% per annum simple interest. His total income in 3 years is Rs. 750. Find the sum invested at different rates of interest.

Accepted Answer

Average rate of interest = (100 * 750) / (5000 * 3) = 5% per annual Investment at 3% per annual = 3 / (3 + 2) × 5000 = Rs. 3000 Investment at 8% per annual = 2 / (3 + 2) × 5000 = Rs. 2000

Question 6

The average daily wages of staff, consisting of supervisors and labourers, of a company is Rs. 50. The average wages of supervisors is Rs. 150 while that of labourers is Rs. 40 per day. If the number of supervisors is 15, find the number of labourer…

Accepted Answer

As per figure we can calculate the ration as below. Number of supervisors / Number of labourers = (10 / 100) = 1/10 Total number of labourers = Total no. of supervisors × 10 = 15 × 10 = 150.

Question 7

A sum of Rs. 70 is divided among 10 children. Each boy gets Rs. 10 whereas a girl gets Rs. 5. If the number of boys is 4, find the number of girls.

Accepted Answer

Number of girls / Number of boys = (3 / 2) Number of girls = (3 / 2) × 4 = 6

Question 8

A vessel contains 80 litres of milk. 16 litres of milk was taken out of the vessel and replaced by water. Then 16 litres of mixture was withdrawn and again replaced by water. The operation was repeated for third time. How much milk is now left in th…

Accepted Answer

Amount of milk left = 80 [1 - (16 / 80)]3 = 80 (4 / 5)3 80 × (64 / 125) = 40.96 liters.

Question 9

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

Accepted Answer

S.P. of 1 kg mixture = Rs. 68.20, Gain % = 10 % Hence, C.P. of 1 kg mixture = (100 / 110) x 68 20 . = Rs. 62 By the rule of alligation Hence, required ratio = 3 : 2

Question 10

A shopkeeper has 100 kgs of tea. He sells a part of it at 20% profit and the rest at 5% loss. If his overall profit is 10%, find the quantity for each part.

Accepted Answer

As per figure, we can calculate as below. Quantity sold at 20% profit = 3 / (3 + 2) × 100 = 60 kgs. Quantity sold at 5% loss = (100 – 60) = 40 kgs.

Question 11

A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?

Accepted Answer

Let A liters wine cask hold originally, then A[1 - (8 / A)]4 / A = 16 / 81 ⇒ (1 - (8 / A))4 = (2 / 3 )4 ⇒ (1 - (8 / A)) = (2 / 3) ⇒ (8 / A) = (1 - (2 /3)) ⇒ (8 / A) = (1 / 3) ∴ A = 24 liters

Question 12

Rs. 675 was divided among 75 boys and girls. Each boy gets Rs. 20 whereas a girl gets Rs. 5. Find the number of boys and girls.

Accepted Answer

Average money per head (boy or girl) = Rs. (675 / 75) = Rs. 9 Number of boys = 4 / (4 + 11) × 75 = 20 Number of girls = 11 / (4 + 11) × 75 = 55.

Question 13

A sum of Rs. 41 was divided among 50 boys and girls. Each boy gets 90 paise and a girl 65 paise. The number of boys is —

Accepted Answer

Question 14

Some amount out of Rs. 7000 was lent at 6 % p.a. and the remaining at 4 % p. a. If the total simple interest from both the fractions in 5 years was Rs. 1600, the sum lent at 6 % p. a. was —

Accepted Answer

Question 15

Sugar at Rs. 15 per kg is mixed with sugar at Rs. 20 per kg in the ratio 2 : 3. Find the price per kg of the mixture—

Accepted Answer

Question 16

Kantilal mixes 80 kg of sugar worth of Rs. 6·75 per kg with 120 kg worth of Rs. 8 per kg. At what rate shall he sell the mixture to gain 20 %?

Accepted Answer

According to question , Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8) Total C. P. of 200 kg of mixture = Rs. 1500 Average rate = Rs. 7·50 per kg Required rate = 120% of Rs. 7·50 Required rate = Rs. 9 per kg.

Question 17

A grocer buys two kind of rice at Rs. 1·80 and Rs. 1·20 per kg respectively. In what proportion should these be mixed, so that by selling the mixture at Rs. 1·75 per kg, 25 % may be gained?

Accepted Answer

Question 18

15 liters of a mixture contains 20 % alcohol and the rest water. If 3 liters of water be mixed in it, the % of alcohol in the new mixture will be —

Accepted Answer

Question 19

A dishonest milkman professes to sell his milk at C. P. But he mixes it with water and thereby gains 25 %. The % of water in the mixture is —

Accepted Answer

Question 20

In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg. So that by selling the mixture at 63 paise per kg he may gain 1 of his out-lay? 6

Accepted Answer

Alligation or Mixture Questions