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Two alcohol-water mixtures A and B of ratio 5 ∶ 1 and 5 ∶ 2 respectively are mixed together in the ratio 3 ∶ 4. On adding 2 ml of alcohol to this mixture, 100 ml of final alcohol-water mixture is obtained. What is the percentage of alcohol in the final mixture?

Two alcohol-water mixtures A and B of ratio 5 ∶ 1 and 5 ∶ 2 respectively are mixed together in the ratio 3 ∶ 4. On adding 2 ml of alcohol to this mixture, 100 ml of final alcohol-water mixture is obtained. What is the percentage of alcohol in the final mixture? Correct Answer 77%

Given:

Alcohol : Water in A = 5 : 1.

Alcohol : Water in B = 5 : 2.

Concept used:

We will be using the concept of ratio.

Calculation:

Quantity of mixture before adding 2 ml alcohol = 100 – 2 = 98 ml

Quantity of mixture A mixed = 3/7 × 98 = 42 ml

∵ Ratio of mixture A = 5 ∶ 1

⇒ Quantity of alcohol in 42 ml of mixture A = 5/6 × 42 = 35 ml

Similarly,

Quantity of mixture B mixed = 4/7 × 98 = 56 ml

∵ Ratio of mixture B = 5 ∶ 2

⇒ Quantity of alcohol in 56 ml of mixture B = 5/7 × 56 = 40 ml

⇒ Quantity of alcohol in 100 ml of final mixture = 35 + 40 + 2 = 77 ml

∴ Percentage of alcohol in final mixture = 77/100 × 100 = 77%

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