A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what ratio should the mixtures in the two bottles be mixed to get a new mixture in which the ratio of spirit to water is 1:3?

Correct option is D

Given:

A bottle contains spirit and water in the ratio 1 ∶ 4

Another identical bottle contains spirit and water in the ratio 4 ∶ 1

Solution:

Let the quantity of the first mixture be x and the quantity of the second mixture be y.

In the first bottle, the ratio of spirit to water is 1 ∶ 4, so the spirit content is x/5 and the water content is 4x/5.

In the second bottle, the ratio of spirit to water is 4 ∶ 1, so the spirit content is 4y/5 and the water content is y/5.

In the new mixture, the spirit content should be (x/5 + 4y/5) and the water content should be (4x/5 + y/5).

The required ratio is 1 ∶ 3, so:

=> (x/5 + 4y/5) / (4x/5 + y/5) = 1/3

=> (x + 4y) / (4x + y) = 1/3

=> 3(x + 4y) = 4x + y

=> 3x + 12y = 4x + y

=> 12y - y = 4x - 3x

=> 11y = x

=> x/y = 11/1

Therefore, the ratio in which the mixtures should be mixed is: (d) 11:1

Short Trick:-