Multiple choice

A cistern can be filled by two pipes filling separately in 12 and 16 minutes respectively. Both pipes are opened together for a certain time but being clogged, only 7/8 of full quantity of water flows through the former and only 5/6 through the latter pipe. The obstructions, however suddenly removed after which the cistern was filled in 3 minutes from that moment. For how long the pipes were clogged?

  1. 4min.

  2. 4½min.

  3. 3½min.

  4. 8⅓min.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the pipes be A and B. Rates are 1/12 and 1/16. Clogged rates are (7/8)(1/12) = 7/96 and (5/6)(1/16) = 5/96. Combined clogged rate = 12/96 = 1/8. Let t be the time clogged. (1/8)*t + (1/12 + 1/16)*3 = 1. (1/8)*t + (7/48)*3 = 1. (1/8)*t + 7/16 = 1. (1/8)*t = 9/16. t = 4.5 minutes.

AI explanation

Let the total capacity be the LCM of 12 and 16, which is 48 units, making the unclogged rates 4 and 3 units per minute respectively for a total of 7. While clogged, they deliver 7/8 and 5/6 of their water, yielding 3.5 and 2.5 units per minute for a clogged total of 6 units per minute. In the final 3 minutes after clearing, the pipes fill at their full rate of 7 units per minute, completing 21 units and leaving 27 units to be filled during the clogged period. Dividing these 27 units by the clogged rate of 6 units per minute gives a clogged duration of 4.5 minutes.

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