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

Question : 1

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 : 2

In what ratio must a person mix three kinds of wheat costing him Rs. 1.20, Rs. 1.44 and Rs. 1.74 per kg, so that the mixture may be worth Rs. 1.41 per kg?

a) 4 : 5 : 7

b) 13 : 7 : 9

c) 1 : 2 : 3

d) 12 : 7 : 7

e) None of these

Answer: (d)

1st wheat 120

2nd wheat 144 3rd wheat 174

following the above rule, we have, [(144 – 141) + (174 – 141)]

[= 141 – 120]

[= 141 – 120]

Therefore, the required ratio = 36 : 21 : 21 = 12 : 7 : 7

Question : 3

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 : 4

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 : 5

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 : 6

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