# alligation or mixture aptitude questions

1. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
A.
 1 3
B.
 1 4
C.
 1 5
D.
 1 7

Explanation:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

 Quantity of water in new mixture = 3 – 3x + x litres 8

 Quantity of syrup in new mixture = 5 – 5x litres 8

 3 – 3x + x = 5 – 5x 8 8

5x + 24 = 40 – 5x

10x = 16

 x = 8 . 5

 So, part of the mixture replaced = 8 x 1 = 1 . 5 8 5

2. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
 A. Rs. 169.50 B. Rs. 170 C. Rs. 175.50 D. Rs. 180

Explanation:

Since first and second varieties are mixed in equal proportions.

 So, their average price = Rs. 126 + 135 = Rs. 130.50 2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

 Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price Rs. 153 Rs. x (x – 153) 22.50

 x – 153 = 1 22.50

x – 153 = 22.50

x = 175.50

3. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is 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. 10 B. 20 C. 21 D. 25

Explanation:

Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

 Quantity of A in mixture left = 7x – 7 x 9 litres = 7x – 21 litres. 12 4

 Quantity of B in mixture left = 5x – 5 x 9 litres = 5x – 15 litres. 12 4

 7x – 21 4
= 7
 5x – 15 + 9 4
9

 28x – 21 = 7 20x + 21 9

252x – 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.

4. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
 A. 4 litres, 8 litres B. 6 litres, 6 litres C. 5 litres, 7 litres D. 7 litres, 5 litres

Explanation:

Let the cost of 1 litre milk be Re. 1

 Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3 4 4

 Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 1 2 2

 Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5 8 8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can    C.P. of 1 litre mixture in 2nd can
 3 4
Mean Price

 5 8
 1 2
 1 8
 1 8

 Ratio of two mixtures = 1 : 1 = 1 : 1. 8 8

 So, quantity of mixture taken from each can = 1 x 12 = 6 litres. 2

5. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
 A. 3 : 7 B. 5 : 7 C. 7 : 3 D. 7 : 5