Multiple choice

Two mixtures A and B of concentration 4:5 and 5:7 of milk to water poured into a vessel in the ratio 3:4. If milk in final mixture is 72 L then find quantity of water in final mixture

  1. 96 L

  2. 88 L

  3. 108 L

  4. 72 L

  5. 84 L
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A Correct answer
Explanation

Mixture A: 3 parts, M:W = 4:5 (4/9 milk). Mixture B: 4 parts, M:W = 5:7 (5/12 milk). Total milk = 3*(4/9) + 4*(5/12) = 4/3 + 5/3 = 3 parts. Total water = 3*(5/9) + 4*(7/12) = 5/3 + 7/3 = 4 parts. If 3 parts = 72 L, 1 part = 24 L. Water = 4 parts = 96 L.

AI explanation

Assume the volumes taken from mixture A and mixture B are 3x and 4x respectively. The milk contributed is 4 over 9 of 3x plus 5 over 12 of 4x, totaling 4x over 3 plus 5x over 3, which equals 3x; since the final milk is 72 litres, 3x equals 72 and x is 24. The water contributed is 5 over 9 of 3x plus 7 over 12 of 4x, totaling 5x over 3 plus 7x over 3, which equals 4x; multiplying 4 by 24 gives 96 litres.

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