Question

Two pipes, A and B, can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

• A. 10 minutes
• B. 12 minutes
• C. 14 minutes
• D. 16 minutes

Hint:

When two pipes fill a tank, their combined rate is the sum of their individual rates.

Answer 1

The Correct Option is B

Step 1: Find the rates of A and B.
Pipe A can fill the tank in 20 minutes, so its rate is: \[ \text{Rate of A} = \frac{1}{20} \text{ tank per minute}. \] Pipe B can fill the tank in 30 minutes, so its rate is: \[ \text{Rate of B} = \frac{1}{30} \text{ tank per minute}. \] Step 2: Find the combined rate.
The combined rate when both pipes are open is the sum of their individual rates: \[ \text{Combined rate} = \frac{1}{20} + \frac{1}{30}. \] Find the LCM of 20 and 30: \[ \text{LCM}(20, 30) = 60. \] So, \[ \text{Combined rate} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}. \] Step 3: Time taken to fill the tank.
The time taken to fill the tank is the reciprocal of the combined rate: \[ \text{Time} = \frac{1}{\frac{1}{12}} = 12 \text{ minutes}. \]