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In three mixtures, alcohol and wine is in the ratio of 1 : 5, 2 : 1 and 3 : 2 respectively. If all the three mixtures are mixed in the ratio of 2 : 3 : 5 respectively. What will be the ratio of alcohol and wine in the resulting mixture?

In three mixtures, alcohol and wine is in the ratio of 1 : 5, 2 : 1 and 3 : 2 respectively. If all the three mixtures are mixed in the ratio of 2 : 3 : 5 respectively. What will be the ratio of alcohol and wine in the resulting mixture? Correct Answer 8 : 7

Given:

Ratio of Alcohol and wine in first mixture = 1 : 5

Ratio of Alcohol and wine in second mixture = 2 : 1

Ratio of Alcohol and wine in third mixture = 3 : 2

Ratio of mixing all the mixture = 2 : 3 : 5

Calculations:

Let the amount of three mixtures be 2a, 3a and 5a respectively.

Amount of alcohol in the resulting mixture = (2a × 1/6 + 3a × 2/3 + 5a × 3/5)

⇒ a/3 + 2a + 3a = 16a/3

Amount of the wine in the resulting mixture = (2a × 5/6 + 3a × 1/3 + 5a × 2/5)

⇒ 5a/3 + a + 2a = 14a/3

Required ratio = 16a/3 : 14a/3

⇒ 16 : 14

⇒ 8 : 7

∴ The ratio of alcohol and wine in the resulting mixture will be 8 : 7.

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