Question

Two pipes A and B can fill a tank in 12 min and 18 min respectively, if both are opened simultaneously then the time taken to fill the tank in minutes is

• A. 8 1/4
• B. 7 1/5
• C. 7 2/5
• D. 8 1/3

Hint:

When two pipes fill a tank together, add their rates (reciprocals of the time) to get the combined rate.

Answer 1

The Correct Option is B

The rate of pipe A is \( \frac{1}{12} \) of the tank per minute, and the rate of pipe B is \( \frac{1}{18} \) of the tank per minute. When both are opened together, the combined rate is: \[ \text{Combined rate} = \frac{1}{12} + \frac{1}{18} = \frac{3 + 2}{36} = \frac{5}{36}. \] Thus, the time taken to fill the tank is the reciprocal of the combined rate: \[ \text{Time} = \frac{36}{5} = 7 \frac{1}{5} \text{ minutes}. \]