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?

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Question: 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

Answer: Option B

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