Multiple choice

A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes (\frac{3}{2}) times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.

  1. 12

  2. 13

  3. 14

  4. 15

  5. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A take x hours. Then B takes (3/2)x hours and C takes 2 × (3/2)x = 3x hours. Combined rate: 1/x + 2/(3x) + 1/(3x) = 1/7. This simplifies to (3+2+1)/(3x) = 1/7, so 6/(3x) = 1/7, giving 2/x = 1/7, therefore x = 14 hours for pipe A alone.

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