Multiple choice

A cistern can be filled by a tap in 8 hours while it can be emptied by another tap in 12 hours. If both taps are opened simultaneously, then after how much time (in hours) will the empty cistern get filled?

  1. 12

  2. 6

  3. 8

  4. 24
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Filling rate = 1/8, emptying rate = 1/12. Net rate = 1/8 - 1/12 = (3-2)/24 = 1/24. The cistern fills in 24 hours.

AI explanation

Using the net work method, the effective rate of filling the cistern is the inlet rate minus the outlet rate: 1 over 8 minus 1 over 12. Finding a common denominator of 24 gives 3 over 24 minus 2 over 24, which equals 1 over 24. The time required to fill the cistern is the reciprocal of this net rate, which is 24 hours.

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