Question

Two taps can separately fill a cistern in $10$ minutes and $15$ minutes, respectively and when the waste pipe is open, they can together fill it in $18$ minutes. The waste pipe can empty the full cistern in:

• A. $7$ min
• B. $9$ min
• C. $13$ min
• D. $23$ min

Answer 1

Answer: (B)

$9$ min

Let us name the $3$ $Taps$ be $T_1,T_2,T_3$

where $T_1,T_2$ are filling pipes and $T_3$ is Waste Pipe.

Water Supplied by $T_1$ in $10$ $min=Volume$ $of$ $Cistern$ $or$ $V$

Water Supplied by $T_1$ in $1$ $min=\frac{V}{10}$

Similarly, Water Supplied by $T_2$ in $15$ $min=V$

Water Supplied by $T_1$ in $1$ $min=\frac{V}{15}$

Let us assume $t$ be the time by $T_3$ to $empty$ Cistern.

Similarly, Water removed from $T_3$ in $1$ $min=\frac{V}{t}$

Now,it is given that they can together fill $V$ in $18$ $minutes$ ($i.e.$ in $1min$ Water supplied $=\frac{V}{18}$ )

$\Rightarrow \frac{V}{10}+\frac{V}{15}-\frac{V}{t}=\frac{V}{18}$

$\Rightarrow \frac{1}{10}+\frac{1}{15}-\frac{1}{t}=\frac{1}{18}$

Solving this Equation we get

$\Rightarrow t=9min$

Therefore Answer is $\left(B\right)$