Mixture and Alligations Exercise I


Ques 1 Mixture & Alligations


Two vessels A and B contain a mixture of milk and water in the ratio 4:5 and 5:1.If both vessels are mixed in the ratio 5:2 then find the ratio of milk and water in new mixture?
  a) 4:5
  b) 5:4
  c) 3:4
  d) 4:3


b is the correct option




Ques 2 Mixture & Alligations


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%?
  a) 3:2
  b) 6:7
  c) 5:6
  d) 2:3


a is the correct option

The answer is a) 3:2.
Let the quantity of tea worth Rs. 60 a kg be x kg and the quantity of tea worth Rs. 65 a kg be y kg.
Then, the cost of x kg of tea worth Rs. 60 a kg = Rs. 60x
The cost of y kg of tea worth Rs. 65 a kg = Rs. 65y
The total cost of the mixture = Rs. 60x + Rs. 65y = Rs. (60x + 65y)
The selling price of the mixture = Rs. (x + y) × 68.20
The profit made by the grocer = Rs. (x + y) × 68.20 - Rs. (60x + 65y)
The profit percentage = (x + y) × 68.20 - Rs. (60x + 65y) / Rs. (60x + 65y) × 100
The grocer wants to make a profit of 10%. So, the profit percentage should be equal to 10.
(x + y) × 68.20 - Rs. (60x + 65y) / Rs. (60x + 65y) × 100 = 10
(x + y) × 68.20 - (60x + 65y) = 0.10 × (60x + 65y)
(x + y) × 68.20 = 1.10 × (60x + 65y)
68.20x + 68.20y = 66x + 71.5y
2.20x = 3.30y
x/y = 3.30/2.20 = 3/2
Therefore, the ratio in which the grocer must mix the two varieties of tea is 3:2.




Ques 3 Mixture & Alligations


200 litres of mixture contains 15% water and the rest is milk. The amount of milk that must be added so that the resulting mixture contains 87.5% milk is?
  a) 30 litres
  b) 35 litres
  c) 40 litres
  d) 45 litres


c is the correct option

The answer is c) 40 litres.

Quantity of milk in 200 litres of the mixture = 85% of 200 litres = (85/100) × 200 = 170 litres.
Let x litres of milk be added to the mixture.
Then, quantity of milk in (200 + x) litres of the new mixture = 170 + x litres.
Milk constitutes 87.5% of the new mixture.
Therefore, (170 + x) / (200 + x) × 100 = 87.5
⇒ 170 + x = (87.5 / 100) × (200 + x)
⇒ 17000 + 100x = 17500 + 87.5x
⇒ 12.5x = 500
⇒ x = 500 / 12.5 = 40 litres.




Ques 4 Mixture & Alligations


A sum of Rs. 41 was divided amount 50 children. Each boy gets 90 paise and each girl 65 paise. The number of boys is?
  a) 32
  b) 34
  c) 36
  d) 38


b is the correct option

The answer is b) 34.

Let the number of boys be x.
Then, the number of girls = (50 - x).
Amount received by each boy = 90 paise.
Amount received by each girl = 65 paise.
Total amount received by all the boys = 90x paise.
Total amount received by all the girls = 65(50 - x) paise.
Total amount received by all the boys and girls = 90x + 65(50 - x) paise.
This is given to be equal to Rs. 41 = 4100 paise.
Therefore, 90x + 65(50 - x) = 4100
⇒ 90x + 3250 - 65x = 4100
⇒ 25x = 850
⇒ x = 850 / 25 = 34.
Therefore, the number of boys is 34.




Ques 5 Mixture & Alligations


A man has 60 pens. He sells some of these at a profit of 12% and the rest at 8% loss. On the whole, he gets a profit of 11%. How many pens were sold at 12% profit?
  a) 47
  b) 52
  c) 55
  d) 57


d is the correct option

The answer is d) 57.

Let x be the number of pens sold at a profit of 12%.
Then, the number of pens sold at a loss of 8% = (60 - x).
Total profit = 11% of 60 = 6.6
Profit on x pens sold at 12% profit = 12% of x = 0.12x
Loss on (60 - x) pens sold at 8% loss = 8% of (60 - x) = 0.08(60 - x)
Therefore, 0.12x - 0.08(60 - x) = 6.6
⇒ 0.20x = 6.6 + 4.8 = 11.4
⇒ x = 11.4 / 0.20 = 57.
Therefore, 57 pens were sold at a profit of 12%.




Ques 6 Mixture & Alligations


A sum of Rs. 6.40 is made up of 80 coins which are either 10-paise or 5-paise coins. How many are coins of 5-paise?
  a) 24
  b) 28
  c) 32
  d) 36


c is the correct option

The answer is c) 32.

Let the number of 5-paise coins be x.
Then, the number of 10-paise coins = (80 - x).
Total value of the coins = Rs. 6.40 = 640 paise.
Value of x 5-paise coins = 5x paise.
Value of (80 - x) 10-paise coins = 10(80 - x) paise.
Therefore, 5x + 10(80 - x) = 640
⇒ 5x + 800 - 10x = 640
⇒ 5x = 160
⇒ x = 160 / 5 = 32.
Therefore, the number of 5-paise coins is 32.




Ques 7 Mixture & Alligations


How much tea at Rs. 4 a kg should be added to 15 kg of tea at Rs. 10 a kg so that the mixture be worth Rs. 6.50 a kg ?
  a) 15 kg
  b) 35 kg
  c) 25 kg
  d) 21 kg


d is the correct option

The correct answer is d) 21 kg.

Let x be the amount of tea at Rs. 4 a kg that should be added to 15 kg of tea at Rs. 10 a kg so that the mixture be worth Rs. 6.50 a kg.
The total cost of the mixture is then 15 * 10 + x * 4 = 150 + 4x.
The total weight of the mixture is 15 + x.
The average price of the mixture is then (150 + 4x) / (15 + x).
We want this to be equal to Rs. 6.50, so we have the equation (150 + 4x) / (15 + x) = 6.50.
Solving for x, we find that x = 21.
Therefore, 21 kg of tea at Rs. 4 a kg should be added to 15 kg of tea at Rs. 10 a kg so that the mixture be worth Rs. 6.50 a kg.