Three pipes A, B and C together can fill a cistern in 6 hours. After working…

20252024202520252025

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

  1. A.

    12

  2. B.

    14

  3. C.

    16

  4. D.

    18

Attempted by 3 students.

Show answer & explanation

Correct answer: B

Key idea: work with rates (fraction of cistern filled per hour).

  1. A, B and C together fill the cistern in 6 hours, so their combined rate is 1/6 of the cistern per hour.

  2. After working together for 2 hours they fill 2 × 1/6 = 1/3 of the cistern. Remaining to fill = 1 − 1/3 = 2/3.

  3. A and B then fill the remaining 2/3 in 7 hours, so the combined rate of A and B is (2/3) ÷ 7 = 2/21 of the cistern per hour.

  4. C's rate = (A+B+C rate) − (A+B rate) = 1/6 − 2/21 = 7/42 − 4/42 = 3/42 = 1/14 of the cistern per hour.

  5. Therefore, time for C alone = reciprocal of its rate = 14 hours.

Answer: 14 hours

Explore the full course: Infosys Preparation