Question

3 Pipes in tank P,Q,R . P and q are inlet pipe and r is outlet . P and q can fill a tank simultanously 12 and 16 minutes . And if we opened 3 pipes together and closed R pipe after some time then all are take 20 minutes to full tank. Then how many time R will take to empty tank.

Answer 1

Given :

p and q are inlet pipe and r is outlet pipe

Time taken by pipe p to fill the tank = 12 min

Time taken by pipe q to fill the tank = 16 min

Total time taken to fill the tank when all three pipes working = 20 min

To Find :

Time taken by pipe r to empty the tank

Solution :

The time taken by pipe r alone to empty the tank = $\dfrac{1}{x}$

The time taken by pipe p alone to empty the tank = $\dfrac{1}{12}$

The time taken by pipe q alone to empty the tank = $\dfrac{1}{16}$

Again

Total time taken to fill the tank when all three pipes working =  time taken by pipe p alone to empty the tank +  time taken by pipe q alone to empty the tank -  time taken by pipe r alone to empty the tank

Total time taken to fill the tank when all three pipes working = $\dfrac{1}{12}$ + $\dfrac{1}{16}$ - $\dfrac{1}{x}$

or,   $\dfrac{1}{12}$  +  $\dfrac{1}{16}$  -  $\dfrac{1}{x}$  =  $\dfrac{1}{20}$

Or,    $\dfrac{4+3}{48}$  -  $\dfrac{1}{x}$  =  $\dfrac{1}{20}$

Or,     $\dfrac{4+3}{48}$  -  $\dfrac{1}{20}$ =  $\dfrac{1}{x}$  

Or,     $\dfrac{7}{48}$  -  $\dfrac{1}{20}$ =  $\dfrac{1}{x}$  

Or ,   $\dfrac{1}{x}$  =   $\dfrac{35 - 12}{240}$

Or,    $\dfrac{1}{x}$  =   $\dfrac{23}{240}$

i.e    x = $\dfrac{240}{23}$

∴     x = 10.43 min = 10 min 25 sec

Hence, The Time taken by pipe r to empty the tank is 10 min 25 sec  Answer

Answer 2

Given:

Time required by P to fill a pipe=12 minutes.

Time required by Q to fill a pipe=16 minutes.

To Find:

Time required to empty the tank.

Solution:

Work done by pipes P and Q:

$\dfrac{1}{12}+\dfrac{1}{16}= \dfrac{4+3}{48}= \dfrac{7}{48}$

The time required to fill the tank=48/7 minutes=6.85 minutes.

Time taken by three pipes to fill the tank (P+Q+R)=20 minutes

$\dfrac{48}{7}+R=20$

$R=20-\dfrac{48}{7}$

$R=\dfrac{140-48}{7}$

R=13.14 minutes

R=-13.14(as it empties the tank)

Therefore, time required to empty the tank=$\dfrac{6.85}{13.14}$=0.521 minutes

=$0.521\times60$

=31.26 seconds.

• Time required to empty the tank=31.26 seconds.