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

Question : 1

A trader has 50 kg of rice, a part of which he sells at 14% profit and the rest at 6% loss. On the whole his loss is 4%. What is the quantity sold at 14% profit and that at 6% loss?

a) 4, 46

b) 7, 43

c) 2, 48

d) 5, 45

e) None of these

Answer: (d)

Question : 2

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can in filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

a) 20

b) 25

c) 10

d) 21

e) None of these

Question : 3

How many kg of salt at 42 P per kg must a man mix with 25 kg of salf at 24 P per kg so that he may, on selling the mixture at 40 P per kg gain 25% on the outlay?

a) 20

b) 30

c) 15

d) 25

e) None of these

Answer: (a)

Cost price of mixture = 40 × ${100}/{125}$P = 32P per kg

By the rule of fraction

Ratio = 4 : 5

Thus, for every 5 kg of salt at 24 P, 4 kg of salt at 42P is used.

∴ the required no. of kg = 25 × $4/5$ = 20.

Question : 4

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 : 5

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 : 6

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