Alligation & Mixtures Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Question : 1

In three vessels each of 10 litres capacity, mixture of milk and water is filled. The ratios of milk and water are 2 : 1, 3 : 1 and 3 : 2 in the three respective vessels. If all the three vessels are emptied into a single large vessel, find the proportion of milk and water in the mixture.

a) 101 : 49

b) 131 : 69

c) 181 : 49

d) 121 : 59

e) None of these

Question : 2

Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69$3/13$% milk, is :

a) 3 : 5

b) 5 : 7

c) 2 : 7

d) 5 : 2

e) None of these

Answer: (c)

Let cost of 1 litre milk be Re. 1.

Milk in 1 litre mix. in B = $8/{13}$ litre, C.P. of a litre mix. in

B = Re. $5/7$.

Milk in 1 litre mix. in B = $5/7$ litre, C.P. of 1 litre mix. in

B = Re. $5/7$

Milk in 1 litre of final mix. = $({{900}/13} × {1/{100}} × 1) = 9/{13}$ litre;

mean price = Re. $9/{13}$

By the rule of alligation, we have:

∴ Required ratio = $2/{91} : 1/{13}$ = 2 : 7

Question : 3

A mixture of certain quantity of milk with 16 litres of water is worth 90 P per litre. If pure milk be worth Rs. 1.08 per litre, how much milk is there in the mixture?

a) 70

b) 90

c) 60

d) 80

e) None of these

Answer: (d)

The mean value is 90 P and the price of water is 0 P.

By the Alligation Rule, Milk and water are in the ratio of 5 : 1.

∴ quantity of milk in the mixture = 5 × 16 = 80 litres.

Question : 4

How much water must be added to a cask which contains 40 litres of milk at cost price Rs. 3.5/litres so that the cost of milk reduces to Rs. 2/litre?

a) 35

b) 50

c) 20

d) 45

e) None of these

Answer: (e)

This question can be solved in so many different ways. But the method of alligation method is the simplest of all the methods. We will apply the alligation on price of milk, water and mixture.

∴ ratio of milk and water should be 2 : 15 = 4 : 3

∴ added water = ${40}/4$ × 3 = 30 litres

Question : 5

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 : 4

b) 4 : 5

c) 3 : 2

d) 3 : 5

e) None of these

Answer: (c)

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%

C.P. of 1 kg of the mixture = Rs. $({100}/{110} × 68.20)$ = Rs. 62.

By the rule of alligation, we have

∴ Required ratio = 3 : 2

Question : 6

In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water? (Weight in gm)

a) 88%

b) 100%

c) 75%

d) 90%

e) None of these