A swimming pool is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is
a. `6\ h r s`
b. `10\ h r s`
c. `15\ h r s`
d. `30\ h r s`

Explanation

To solve the problem, let's denote the time taken by the first pipe to fill the pool as \( x \) hours.

1. **Define the time taken by each pipe:**
- Time taken by the first pipe = \( x \) hours
- Time taken by the second pipe = \( x - 5 \) hours (since it fills the pool 5 hours faster than the first pipe)
- Time taken by the third pipe = \( x + 4 \) hours (since the second pipe is 4 hours slower than the third pipe)

2. **Set up the equation based on the problem statement:**
...