Question

Two pipes A and B can independently fill a cistern in 12 minutes and 18 minutes respectively. A third pipe C can empty the same cistern when full in 9 minutes. If all three pipes A, B, and C are opened together, in how many minutes will the cistern be empty?

• A. \(40\)
• B. \(36\)
• C. \(35\)
• D. \(32\)

Hint:

Treat filling rates as positive and emptying rates as negative while finding the net rate.

Answer 1

The Correct Option is B

Step 1: Determine individual rates. A fills: \[ \frac1{12} \] B fills: \[ \frac1{18} \] C empties: \[ \frac1{9} \]

Step 2: Find net rate. \[ \frac1{12}+\frac1{18}-\frac1{9} \] LCM \(=36\) \[ =\frac3{36}+\frac2{36}-\frac4{36} \] \[ =\frac1{36} \] Thus the cistern is filled at \[ \frac1{36} \] of its capacity per minute. Hence time required: \[ 36 \text{ minutes} \] \[ \boxed{36} \]