Multiple choice

A vessel contains liquid P and Q in the ratio 5:3. If 16 litres of the mixture are removed and the same quantity of liquid Q is added, the ratio become 3:5. What quantity does the vessel hold?

  1. 35 litres

  2. 45 litres

  3. 40 litres

  4. 50 litres

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial P=5x, Q=3x. Total=8x. Removing 16L removes 10L of P and 6L of Q. Remaining: P=5x-10, Q=3x-6+16=3x+10. Ratio (5x-10)/(3x+10) = 3/5. 25x-50 = 9x+30, 16x=80, x=5. Total = 8*5 = 40 litres.

AI explanation

Let the initial volume of the vessel be V; the amount of liquid P removed is (5/8) * 16 = 10 L, and the amount of liquid Q removed is (3/8) * 16 = 6 L. After adding 16 L of liquid Q, the new amounts are P = 5V/8 - 10 and Q = 3V/8 - 6 + 16 = 3V/8 + 10. Set the new ratio to 3:5: (5V/8 - 10) / (3V/8 + 10) = 3/5. Solving this yields 25V - 400 = 9V + 240, which simplifies to 16V = 640 and V = 40. The vessel holds 40 litres.

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