Question

A cistern can be filled by a tap in 6 hours and emptied by an outlet pipe in 7.5 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?

• A. 24 hours
• B. 25 hours
• C. 27 hours
• D. 30 hours

Answer 1

Answer:

D. 30 hours

It will take 30 hours to fill the cistern when both the tap and the outlet pipe are opened together.

* Tap filling rate: The tap fills $\frac{1}{6}$ of the cistern per hour.

* Outlet pipe emptying rate: The outlet pipe empties $\frac{1}{7.5}$ (or $\frac{2}{15}$) of the cistern per hour.

Net work done in 1 hour:

$\text{Net Rate} = \frac{1}{6} - \frac{2}{15}$

To subtract these fractions, find a common denominator (which is 30):

$\text{Net Rate} = \frac{5}{30} - \frac{4}{30} = \frac{1}{30}$

Since $\frac{1}{30}$ of the cistern is filled every hour, the total time required to fill it completely is the reciprocal of the net rate:

$\text{Total Time} = 30\text{ hours}$