Multiple choice

Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern is:

  1. 14

  2. 12

  3. 15

  4. 18

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

Let P, Q, R fill the cistern in a, b, c hours respectively. Combined rate: 1/a + 1/b + 1/c = 1/6. After 2 hours, 2/6 = 1/3 filled, 2/3 remains. P and Q fill 2/3 in 7 hours: (1/a + 1/b) × 7 = 2/3, so 1/a + 1/b = 2/21. Subtracting from first equation: (1/a + 1/b + 1/c) - (1/a + 1/b) = 1/6 - 2/21. Thus 1/c = 1/14, so c = 14 hours.

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