Question

Pipe A can fill a cistern in 18 minutes. Pipe B can fill the cistern in 24 minutes. Pipe C can empty the cistern in 36 minutes. At 10 a.m., pipe A is opened. At 10 :
10 a.m, pipe C is opened. At 10 : 15 a.m, pipe B is opened. The time at which the
cistern would be full is approximately​

Answer 1

Answer:

10:20

Step-by-step explanation:

correct answer is 10:20

Answer 2

Pipe and Cistern

Given:

Pipe A can fill a cistern in 18 minutes.

Pipe B can fill the cistern in 24 minutes.

Pipe C can empty the cistern in 36 minutes.

Pipe A is opened at 10:00 a.m.

Pipe B is opened at 10:15 a.m.

Pipe C is opened at 10:10 a.m.

To find:

Time at which cistern will be full.

Explanation:

Let the work done by pipe A in 1 min is  $\frac{1}{18}$.

Let the work done by Pipe B in 1 min is $\frac{1}{24}$.

Let the work done by pipe C in 1 min is $-\frac{1}{36}$.(negative sign to denote that this pipe empties the cistern)

According to question,

$15(\frac{1}{18})+ 5(-\frac{1}{36})+x(\frac{1}{18} +\frac{-1}{36}+ \frac{1}{24})=1\\\\\implies (\frac{15}{18} -\frac{5}{36}+\frac{5x}{72} )=1$

$\implies \frac{25}{36} +\frac{5x}{72} =1\\\\\implies \frac{5x}{72} =\frac{11}{36}\\\\x=4.4$

Hence after 10:15 a.m. all pipes works for 4.4 minutes.

So, the cistern will be full by 10:15 added with 4.4 minutes.

As answer needs to be in approximation, so cistern will be filled by 10.20 a.m.