Sainik School Entrance Exam 2020 Solved Paper

(c) If, both pipes are opened at $6\mathrm{AM}$ and tank is full at $8\mathrm{PM}$
∴ Time = From $6\mathrm{AM}$ to $8\mathrm{AM}$
$=12+2=14$ hours
Suppose that B be closed after $\mathit{x}$ hours
Then, part filled by A in 14 hours $-$ part emptied by B in $\left(14-\mathit{x}\right)$ hours $=1$
$\Rightarrow \frac{14}{12}-\frac{14-\mathit{x}}{18}=1$
$\Rightarrow \frac{7}{6}-\frac{14-\mathit{x}}{18}=1$
$\Rightarrow \frac{21-\left(14-\mathit{x}\right)}{18}=1$
$\Rightarrow \frac{21-14+\mathit{x}}{18}=1$
$\Rightarrow 7+\mathit{x}=18$
$\Rightarrow \mathit{x}=18-7=11\mathrm{hrs}$.
∴ The pipe B is closed at $6\mathrm{AM}+\left(14-\mathit{x}\right)\mathrm{hr}$
$=6\mathrm{AM}+\left(14-11\right)\mathrm{hr}$
$=6\mathrm{AM}+3\mathrm{hr}=9\mathrm{AM}$
Hence, the pipe is closed at $9\mathrm{AM}$