Multiple choice

Q. 10. A cask contains a mixture of two liquids P and Q in the ratio 7 : 5. When 6 L of this mixture is taken out from the cask and an equal volume is filled with Q, the ratio of P and Q becomes 21 : 19. Find the initial volume of the mixture in the cask.

  1. 30L

  2. 45L

  3. 60L

  4. 42L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial volume be V. Liquid P = 7/12 V, Q = 5/12 V. Removing 6L removes 3.5L of P and 2.5L of Q. Remaining: P = 7/12 V - 3.5, Q = 5/12 V - 2.5. Adding 6L of Q: P = 7/12 V - 3.5, Q = 5/12 V + 3.5. Ratio (7/12 V - 3.5) / (5/12 V + 3.5) = 21/19. Solving for V gives 60L.

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