Question

A cistern can be filled by two pipes a and b in 10 and 15 hours respectively and is then emptied by a tap in 8 hours. if all the taps are opened, the cistern will be fill in:

Answer 1

If all the taps are opened, the cistern will be fill in 24 hours

Solution:

Pipe a fill the cistern in 10 hours,

So pipe can fill in 1 hour $\left(\frac{1}{10}\right)$ part of the cistern

Pipe b fill the cistern in 15 hours,

So pipe can fill in 1 hour $\left(\frac{1}{15}\right)$ part of the cistern

Tap can empty the cistern in 8 hours

Sp tap can empty in 1 hour $\left(\frac{1}{8}\right)$ of the cistern

Now if all the pipes and tap are open, in 1 hour it can be filled $=\left(\frac{1}{10}+\frac{1}{15}-\frac{1}{8}\right)=\left(\frac{5}{120}\right)=\frac{1}{24}$

So in 1 hour $\frac{1}{24}$ of the cistern will be filled

Hence, the time to fill the full cistern is 24 hours.