Question

Choose the correct answer from the alternatives given.
A and B are two taps which can fill a tank individually in 8 and 10 minutes respectively. However, there is a leakage at the bottom, which can empty a filled tank in 40 minutes. If the tank is empty initially, how much time will both the taps take to fill the tank (leakage is still there)?

• A. 6 min.
• B. 8 min.
• C. 6$\frac{1}{2}$ min.
• D. 5 min.

Answer 1

Answer: (D)

The correct option is D 5 min.
Let the capacity of the tank be 40 (LCM of 8, 10 & 40).
A fills = $\frac{40}{8}$ = 5 units / minute.
B fills = $\frac{40}{10}$ = 4 units / minute.
C empties = $\frac{40}{40}$ = -1 unit / minute.
(A + B + C)s per minute work = 5 + 4 - 1 = 8 units/min.
Time taken by (A + B + C) together to fill the tank = $\frac{40}{8}$ = 5 minutes.