Question

Pipe A when open alone can fill the tank in 20 hours. Pipe B when open alone can fill the tank in 10 hours. When A, B, and C are open together, the tank will be full after 7.5 hours. How many hours will be taken by pipe C when open alone to empty the full tank?

• A. 30 hours
• B. 45 hours
• C. 60 hours
• D. 90 hours

Hint:

If a pipe empties, its rate is negative when combined with filling pipes.
Calculate individual rates carefully and subtract to find emptying pipe rate.

Answer 1

The Correct Option is C

Step 1: Calculate individual rates
- Rate of A = $\frac{1}{20}$ tank/hour
- Rate of B = $\frac{1}{10}$ tank/hour
Step 2: Calculate combined rate of A, B, and C
Combined rate of A, B, and C = $\frac{1}{7.5} = \frac{2}{15}$ tank/hour
Step 3: Calculate rate of C
Rate of C = Combined rate - Rate of A - Rate of B
= $\frac{2}{15} - \frac{1}{20} - \frac{1}{10}$
Find common denominator (60):
$\frac{2}{15} = \frac{8}{60}$, $\frac{1}{20} = \frac{3}{60}$, $\frac{1}{10} = \frac{6}{60}$
Rate of C = $\frac{8}{60} - \frac{3}{60} - \frac{6}{60} = \frac{-1}{60}$ tank/hour
Since rate is negative, pipe C empties the tank at the rate of $\frac{1}{60}$ tank/hour.
Step 4: Time taken by pipe C to empty the tank
Time = $\frac{1}{\text{Rate}} = 60$ hours
Therefore, pipe C will take 60 hours to empty the tank.