Multiple choice

Pipes, $A, B$ and $C$ are attached to a cistern $A$ and $B$ can fill it in $20$ min and $30$ respectively, while $C$ can empty it in $15$ min $H A, B$ and $C$ kept in operation successively for $1$ minute each, how soon will the cistern be filled?

  1. $167$ min
  2. $160$ min
  3. $166$ min
  4. $164$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In each three-minute cycle, pipes A, B, and C contribute 1/20 + 1/30 - 1/15 = 1/60 of the cistern. After 55 complete cycles, 165 minutes have passed and 1/12 remains. Pipe A fills this remainder in 2.5 minutes, so the cistern fills during the next cycle at 167.5 minutes, making 167 minutes the intended option under whole-minute timing.

AI explanation

Let the total capacity be 60 units, giving rates of 3 units/min for A, 2 units/min for B, and -4 units/min for C. In a 3-minute cycle, the net work done is 3 + 2 - 4 = 1 unit. In 165 minutes, which is 55 such cycles, 55 units are filled, leaving 5 units to be filled. Pipe A fills 3 units in the 166th minute, and pipe B fills the remaining 2 units in the 167th minute. The result is 167 min.

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