Fill pipe P is 21 times faster than fill pipe Q. If Q can fill a cistern in 110 minutes, find the time it takes to fill the cistern when both fill pipes are opened together.

The correct option is 5 minutes.

Step-by-step explanation:

1. Determine the rate of fill pipe Q:
Since pipe Q can fill the cistern in 110 minutes, the rate at which Q fills the cistern per minute is:
${\mathrm{Rate}}_Q=\frac{1}{110}$

2. Determine the rate of fill pipe P:
We are given that pipe P is 21 times faster than pipe Q. Thus, the rate at which P fills the cistern per minute is:
${\mathrm{Rate}}_P=21\times {\mathrm{Rate}}_Q=21\times \frac{1}{110}=\frac{21}{110}$

3. Calculate the combined rate when both pipes work together:
When both pipes are opened simultaneously, their combined filling rate per minute is the sum of their individual rates:
${\mathrm{Rate}}_{P+Q}=\frac{21}{110}+\frac{1}{110}$
${\mathrm{Rate}}_{P+Q}=\frac{22}{110}$
Simplifying the fraction by dividing both the numerator and the denominator by 22:
${\mathrm{Rate}}_{P+Q}=\frac{1}{5}$

4. Find the total time to fill the cistern:
The time required to fill the cistern is the reciprocal of their combined filling rate:
$\mathrm{Time}=\frac{1}{{\mathrm{Rate}}_{P+Q}}=\frac{1}{1/5}=5$
Thus, it takes 5 minutes to fill the cistern when both pipes are opened together.