Question

Tap A can fill the tank in two hours while taps B and C can empty it in six and eight hours respectively. All the taps remained open initially. After two hours tap C was closed and after one more hour tap B was also closed. In how much time now would the remaining tank get filled ?

• A. 12 min
• B. 15 min
• C. 30 min
• D. 20 min

Answer 1

The correct option is C 30 min

Let us name the $3$ $Taps$ be $T_A,T_B,T_C$

where $T_B,T_C$ are emptying pipes and $T_A$ is filling Pipe.

Water Emptied by $T_B$ in $6$ $hours=Volume$ $of$ $Tank$ $or$ $V$

Water Emptied by $T_B$ in $1$ $Hour=\frac{V}{6}$

Similarly, Water Emptied by $T_C$ in $8$ $Hour=V$

Water Emptied by $T_C$ in $1$ $Hour=\frac{V}{8}$

Similarly, Water Supplied by $T_A$ in $2$ $Hour=V$

Water Supplied by $T_A$ in $1$ $Hour=\frac{V}{2}$

After 2 Hours,

$\Rightarrow 2\frac{V}{2}-2\frac{V}{8}-2\frac{V}{6}=\frac{5V}{12}$

After 3 Hours,

$\Rightarrow \frac{5V}{12}+\frac{V}{2}-\frac{V}{6}=\frac{3V}{4}$

Now, only $T_A$ is opened

Remaining Volume$=V-\frac{3V}{4}$ $=\frac{V}{4}$

Now Time taken to Fill Remaining Tank

$\Rightarrow \frac{\frac{V}{4}}{\frac{V}{2}}=\frac{1}{2}hrs=30min$

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