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Two pipes $P$ and $Q$ can fill a tank in $6$ hours and $9$ hours respectively, while a third pipe $R$ can empty the tank in $12$ hours.  Initially, $P$ and $R$ are open for $4$ hours, Then $P$ is closed and $Q$ is opened. After $6$ more hours $R$ is closed. The total time taken to fill the tank (in hours) is  ____

  1. $13.50$
  2. $14.50$
  3. $15.50$
  4. $16.50$
in Numerical Ability by Veteran (416k points)
edited by | 59 views
Migrated from GO Mechanical 2 months ago by Arjun

2 Answers

+1 vote
Best answer

P can fill the tank in $6$ hours

$\Rightarrow$ In $1$ hr P can fill $\frac{1}{6}$ of the tank.

Q can fill the tank in $9$ hours

$\Rightarrow$ In $1$ hr Q can fill $\frac{1}{9}$ of the tank.

R can empty the tank in $12$ hours

$\Rightarrow$ In $1$ hr R can empty $\frac{1}{12}$ of the tank.


P and R are opened for $4$ hours

$\Rightarrow$ They fill $4*\left ( \frac{1}{6}-\frac{1}{12} \right ) = 4*\frac{1}{12}=\frac{1}{3}$ of the tank.

$\Rightarrow$ $1-\frac{1}{3}=\frac{2}{3}$ of the tank is still empty.


Then P is closed and Q is opened. After $6$ more hours R is closed.

$\Rightarrow$ Q and R are opened together for $6$ hours.

$\Rightarrow$ They fill $6*\left ( \frac{1}{9}-\frac{1}{12} \right ) = 6*\frac{1}{36}=\frac{1}{6}$ of the tank.

$\Rightarrow$ $\frac{2}{3}-\frac{1}{6}=\frac{4-1}{6}=\frac{1}{2}$ of the tank is still empty.


Now only Q is opened

$\because$ Q can fill a tank in $9$ hr

$\Rightarrow$ Q can fill $\frac{1}{2}$ of the tank in $9*\frac{1}{2}$ hours $=4.5$ hours.


$\therefore$ Total Time to fill the tank $=4$ hours $+6$ hours $+ 4.5$ hours $=14.5$ hours

So, Option B. $14.50$  is the correct answer.

by Boss (17.5k points)
edited by
+2
There is a mistake in the last step. Q can fill tank in 9 hours. So, answer would be 4+6+4.5=14.5 hours. Hence, B is the answer.
+1
Corrected now :)
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by (341 points)
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