Question

Two pipes A and B can fill a tank in 10 minutes and 15 minutes respectively. Both pipes are opened together, but after 3 minutes, pipe B is closed. How much more time will it take for pipe A to fill the remaining part of the tank?

• A. 7 minutes
• B. 4 minutes
• C. 3 minutes
• D. 5 minutes

Hint:

When pipes work together, always find the "unit rate" (amount of work done per minute) first. Remember to subtract the work already completed from the total work (which is 1) to find the remaining task.

Answer 1

The Correct Option is D

Concept: This is a work-rate problem. We calculate the rate at which each pipe fills the tank (fraction of the tank filled per minute) and then determine how much work is completed when both are working, followed by the remaining work for pipe A.

Step 1: Calculate the work rates of pipes A and B.
The work rate is the reciprocal of the time taken to fill the tank completely. \[ \text{Work rate of Pipe A} = \frac{1}{10} \text{ tank per minute} \] \[ \text{Work rate of Pipe B} = \frac{1}{15} \text{ tank per minute} \]

Step 2: Calculate the combined work rate when both pipes are open.
\[ \text{Combined Rate} = \frac{1}{10} + \frac{1}{15} = \frac{3+2}{30} = \frac{5}{30} = \frac{1}{6} \text{ tank per minute} \]

Step 3: Calculate the work done in the first 3 minutes.
\[ \text{Work done} = \text{Combined Rate} \times \text{Time} = \frac{1}{6} \times 3 = \frac{3}{6} = \frac{1}{2} \text{ of the tank} \]

Step 4: Calculate the remaining work.
\[ \text{Remaining work} = 1 - \frac{1}{2} = \frac{1}{2} \text{ of the tank} \]

Step 5: Calculate the time taken by pipe A to finish the remaining work.
\[ \text{Time taken by A} = \frac{\text{Remaining work}}{\text{Rate of A}} = \frac{1/2}{1/10} = \frac{1}{2} \times 10 = 5 \text{ minutes} \] \centerline{{5 minutes}}