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

Question : 1

A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed in that chemical so that after selling the mixture at Rs. 20/litre he may get a profit of 25%?

a) 15

b) 17

c) 14

d) 16

e) None of these

Question : 2

Milk and water are mixed in a vessel A in the proportion 5 : 2, and in vessel B in the proportion 8 : 5. In what proportion should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion of 9 : 4?

a) 5 : 7

b) 7 : 9

c) 4 : 5

d) 7 : 2

e) None of these

Answer: (d)

In vessel A, milk = $5/7$ of the weight of mixture

In vessel B, milk = $8/{13}$ of the weight of mixture. Now, we

want to form a mixture in which milk will be $9/{13}$ of the weight of this mixture.

By alligation rule:

∴ required proportion is $1/{13} : 2/{91}$ = 7 : 2

Question : 3

300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?

a) 50 gm

b) 70 gm

c) 40 gm

d) 60 gm

e) None of these

Answer: (d)

The existing solution has 40% sugar. And sugar is to be mixed;

so the other solution has 100% sugar. So, by alligation method:

∴ The two mixtures should be added in the ratio 5 : 1.

Therefore, required sugar = ${300}/5$ × 1 = 60 gm

Question : 4

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 : 5

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 : 6

In a mixture of 60 litres, the ratio of milk to water is 2 : 1. If the ratio of milk to water is to be 1 : 2, then amount of water to be further added is ___________.

a) 40

b) 80

c) 20

d) 60

e) None of these

Answer: (d)

Apply the alligation on fraction of milk in each mixture.

Ratio of mixture to water = 1 : 1

Therefore, if there is 60 liture of solution, 60 litres of water should be added.