Multiple choice

The ratio of milk and water in A and B is 5 : 3 and 4 : 3 respectively. The quantity of A and B is 40 lit and 84 lit respectively. After adding X lit of pure milk to mixture B the ratio of milk and water becomes 16 : 9. If A and B are mixed, what is the amount of milk in the final mixture?

  1. 84

  2. 150

  3. 120

  4. 89
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mixture B has 84 liters with ratio 4:3 (48 milk, 36 water). Adding X liters of milk makes the ratio 16:9. (48+X)/36 = 16/9. 9(48+X) = 576, 432 + 9X = 576, 9X = 144, X = 16. Total milk = (5/8 * 40) + (48 + 16) = 25 + 64 = 89.

AI explanation

When A and B are mixed without adding milk X, the total milk is 40 * (5/8) + 84 * (4/7), equaling 25 + 48 = 73 liters, and the total water is 40 * (3/8) + 84 * (3/7), equaling 15 + 36 = 51 liters. However, solving for X using the condition (48 + X) / 36 = 16 / 9 yields 432 + 9X = 576, so 9X = 144 and X = 16. Adding this 16 liters of pure milk to the 73 liters of original milk gives a final amount of 89 liters.

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