Question

A water tank has three taps A, B, and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour, and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

• A. 120 litres
• B. 240 litres
• C. 180 litres
• D. 60 litres

Hint:

Always convert each tap’s rate to the same unit (buckets/min), sum them for combined rate, multiply by total time, and finally convert to litres.

Answer 1

The Correct Option is B

First, find each tap’s filling rate in buckets per minute:
Tap A: 4 buckets in 24 minutes $\Rightarrow$ $\frac{4}{24} = \frac{1}{6}$ bucket/min.
Tap B: 8 buckets in 60 minutes $\Rightarrow$ $\frac{8}{60} = \frac{2}{15}$ bucket/min.
Tap C: 2 buckets in 20 minutes $\Rightarrow$ $\frac{2}{20} = \frac{1}{10}$ bucket/min.
Together, their combined rate = $\frac{1}{6} + \frac{2}{15} + \frac{1}{10}$.
Find LCM of 6, 15, 10 = 30. Convert: $\frac{5}{30} + \frac{4}{30} + \frac{3}{30} = \frac{12}{30} = \frac{2}{5}$ bucket/min.
If all taps are opened together, in 2 hours (120 minutes), total buckets filled = $120 \times \frac{2}{5} = 48$ buckets.
If each bucket holds 5 litres, total capacity = $48 \times 5 = 240$ litres.
Thus, the capacity of the tank is $\boxed{240 \ \text{litres}}$.