Question

A swimming pool is fitted with three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time as that taken by the third pipe alone. The second pipe fills the pool $5hours$ faster than the first pipe and $4hours$ slower than the tired pipe. Find the time required by the third pipe to fill the pool.

• A. $10hours$
• B. $6hours$
• C. $16hours$
• D. $5hours$

Answer 1

The correct option is B $6hours$

Let the time required to fill the three pipes be $a,b$ and $c$ hours.

In $1$ hour, they respectively fill $\frac{1}{a},\frac{1}{b}$ and $\frac{1}{c}$ part of the pool.

According to the condition,

$\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$

$\Rightarrow \frac{b+a}{ab}=\frac{1}{c}$ ....(1)

$a-b=5$

$\Rightarrow a=b+5$ ....(2)

and $b-c=4$

$\Rightarrow c=b-4$ ....(3)

Substituting the value of $a$ and $c$ in equation (1), we get

$\frac{b+(b+5)}{(b+5)\times b}=\frac{1}{b-4}$

After solving this, we get

$b=10,b=-2$

We need to neglect $b=-2$.

Thus $b=10$ is correct.

Substituting this value in equations (2) and (3),

$a=10+5=15$ and $c=10-4=6$

Therefore, time required for the first pipe $=15$ hours,

time required for the second pipe $=10$ hours

and time required for the third pipe $=6$ hours.