The ratios of alcohol to water in solutions A and B are 1:3 and 3:1, respectively. Solutions A and B are mixed in the ratio 1:1. In 400 ml of the resulting solution, how much water (in ml) should be mixed to obtain a solution in which the ratio of alcohol to water is 1:2?
Show answer & explanation
Correct answer: C
Explanation
Given:
Solution A: Alcohol : Water = 1 : 3
Solution B: Alcohol : Water = 3 : 1
A : B = 1 : 1
Mixture = 400 ml
Formula:
Amount in mixture = Total amount × Ratio / Total proportion
Alcohol in A = 1/4, Water = 3/4
Alcohol in B = 3/4, Water = 1/4
Alcohol's share = (1/4 + 3/4) / 2 = 1/2
Water's share = (3/4 + 1/4) / 2 = 1/2
In a 400 ml mixture
Alcohol = 200 ml
Water = 200 ml
Let x ml of water be added.
New ratio:
200 : (200 + x) = 1 : 2
2 × 200 = 200 + x
400 = 200 + x
x = 200 ml water must be added.