Multiple choice

A tank holds a mixture of two liquids, P and Q, in the ratio 5 : 7. If 14 litres of Q are drained and replaced with 12 litres of P, the new ratio of P to Q becomes 3 : 2. What is the initial quantity of liquid Q in the tank?

  1. 30 litres

  2. 42 litres

  3. 49 litres

  4. 56 litres

  5. 63 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: P=5x, Q=7x. (5x + 12) / (7x - 14) = 3/2. 10x + 24 = 21x - 42. 11x = 66, x = 6. Initial Q = 7 * 6 = 42 litres.

AI explanation

Let the initial quantities of P and Q be 5x and 7x. When 14 liters of Q are removed, Q becomes 7x - 14, and adding 12 liters of P makes P become 5x + 12. The new ratio gives (5x + 12) / (7x - 14) = 3 / 2, which means 10x + 24 = 21x - 42. Solving for x yields 11x = 66, so x = 6, and the initial quantity of Q was 7 * 6 = 42 litres.

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