Question

Two pipes a and b can independently fill a tank in 20 and 30 minutes respectively. a third pipe c can empty the tank completely in 15 minutes. if all the pipes are kept open together, how long will it take for the tank to get filled completely?

Answer 1

In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as

Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30

Part filled by (A+B) in 1 min = 1/20 + 1/30
= 1/12

So both pipes can fill the tank in 12 mins.

Answer 2

Time required  to get filled  tank completely if all the pipes are kept open together is 1 hrs.

Step-by-step explanation:

Given:

Pipes a can independently fill a tank in 20 minutes.

Pipes  b can independently fill a tank in 30 minutes.

Pipe c can empty the tank completely in 15 minutes.

To Find:

Time required  to get filled  tank completely if all the pipes are kept open together,

Formula Used:

If a pipe requires 'k' hours to fill up the tank, then part filled in 1 hr =$\frac{1}{k}$

If a pipe requires 'n' hours to empty the full tank, then part emptied in      1 hr = $\frac{1}{n}$

Solution:

Quantity of water filled in  tank by the a  pipe in one minute = $\frac{1}{20}$

Quantity of water filled  in  tank by the b pipe  in one minute =$\frac{1}{30}$

Quantity of water emptied from tank  by the c pipe in one minute = $\frac{1}{15}$

Quantity of water filled in tank in  one minute, when all the 3 pipes are opened = $\frac{1}{20} +\frac{1}{30} -\frac{1}{15}$

             = $\frac{3+2-4}{60}$

             =  $\frac{1}{60}$                                                                                                              

                                                                                                                           

Time required  to get filled  tank =  $\frac{1}{\frac{1}{60} }$   = 60 minutes

                                                                 = 1 hour

                                                                                                       

Thus, Time required  to get filled  tank completely if all the pipes are kept open together is 1 hrs.