Multiple choice

There are two container A and B. A contains mixture of milk and water in the ratio 3:Y and B contains 75 L of pure water only. 75 L of mixture from A is taken out and mixed in B so that final ratio of milk and water in the B is 3 : 7. Find value of Y.

  1. 7

  2. 5

  3. 1

  4. 2

  5. 4
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D Correct answer
Explanation

Mixture A has milk/water ratio 3:Y. 75L of A contains 75 * 3/(3+Y) milk and 75 * Y/(3+Y) water. Added to 75L of pure water, total milk = 225/(3+Y), total water = 75 + 75Y/(3+Y). Ratio 3:7 implies 225/(3+Y) / (75 + 75Y/(3+Y)) = 3/7. Solving gives Y=2.

AI explanation

When 75 litres of mixture is taken from vessel A, it contains 75 multiplied by 3 over (3 plus Y) milk and 75 multiplied by Y over (3 plus Y) water. Vessel B initially has 75 litres of pure water, so its new water content is 75 plus 75Y over (3 plus Y). Since the final ratio of milk to water in B is 3 to 7, the ratio of 225 over (3 plus Y) to 75 plus 75Y over (3 plus Y) equals 3 over 7. Solving this equation gives 75(3 plus Y) equals 225 plus 75Y, which simplifies to Y equals 2.

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