Pipes A and B can fill a tank in 20 hours and 30 hours respectively. Pipe C is…

2023

Pipes A and B can fill a tank in 20 hours and 30 hours respectively. Pipe C is an outlet pipe. When all three pipes are opened together, 2/9 of the tank is filled in 8 hours.

Pipe C alone can empty 1/3 of the tank in:

  1. A.

    4 hours

  2. B.

    3 hours

  3. C.

    5 hours

  4. D.

    6 hours

Attempted by 7 students.

Show answer & explanation

Correct answer: D

Concept: In pipe-and-cistern problems, assume the tank's total capacity equals the LCM of every time value given in the question, including the denominator of any given fraction of work done, so that each pipe's rate becomes a whole number of units per hour. When filling pipes and an emptying (outlet) pipe run together, the net rate equals the sum of the filling rates minus the emptying rate.

Application (LCM method):

  1. Take the tank's capacity as LCM(20, 30, 9) = 180 units (9 is included because the given filled fraction is 2/9).

  2. Rate of Pipe A = 180 ÷ 20 = 9 units/hour.

  3. Rate of Pipe B = 180 ÷ 30 = 6 units/hour.

  4. Combined rate of A and B = 9 + 6 = 15 units/hour.

  5. With all three pipes open, 2/9 of the tank = (2/9) × 180 = 40 units is filled in 8 hours, so the net rate = 40 ÷ 8 = 5 units/hour.

  6. Since net rate = (Rate of A + Rate of B) − Rate of C, 5 = 15 − Rate of C, giving Rate of C = 10 units/hour.

  7. To empty one-third of the tank = (1/3) × 180 = 60 units, the time taken = 60 ÷ 10 = 6 hours.

Cross-check (fraction method): Rate of A + Rate of B = 1/20 + 1/30 = 1/12 tank/hour. Net rate = (2/9) ÷ 8 = 1/36 tank/hour. So Rate of C = 1/12 − 1/36 = 1/18 tank/hour, and time to empty 1/3 of the tank = (1/3) ÷ (1/18) = 6 hours — the same result.

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