Question

A tank can be filled by two taps A and B in 12 hours separately. The full tank can be emptied by a third tap in 8 hours. If all the taps are turned on at the same time, then the time taken to fill the empty tank will be:

• A. 24 hours
• B. 48 hours
• C. 38 hours
• D. 35 hours

Hint:

For problems involving filling and emptying rates, sum up the rates (positive for filling, negative for emptying) and then take the reciprocal to find the total time.

Answer 1

The Correct Option is A

Given: - Tap A fills in 12 hours → Rate = \( \frac{1}{12} \) - Tap B fills in 12 hours → Rate = \( \frac{1}{12} \) - Tap C empties in 8 hours → Rate = \( -\frac{1}{8} \) Total rate when all taps are open: \[ \frac{1}{12} + \frac{1}{12} - \frac{1}{8} \] Convert to a common denominator (LCM = 24): \[ \frac{2}{12} = \frac{4}{24}, \quad \frac{1}{8} = \frac{3}{24} \] \[ \text{Net rate} = \frac{4}{24} - \frac{3}{24} = \frac{1}{24} \] Time required to fill the tank: \[ \frac{1}{\frac{1}{24}} = 24 \text{ hours} \]
Thus, the correct answer is 24 hours.