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.

Correct option is A

Given:

Time taken by pipe Q to fill the tank = 110minutes

Time taken by pipe P to fill the tank = 21 times faster than Q

Formula Used:

Let total work to fill the tank be 1.

Then work done by a pipe in 1 hour =$$\frac{1}{Total\ time\ to\ fill}$$​​

Solution:

Work done by Q in 1 minute will be $$\frac{Total\ Work}{Total\ time\ } =\frac{1}{110}$$​​

Work done by P in 1 minute will be $$\frac{Total\ Work}{Total\ time} =\frac{1}{110}\times 21 = \frac{21}{110}$$​​

Work done by pipes P and Q together in 1 minute will be = $$\frac{1}{110} + \frac{21}{110} = \frac{1+21}{110} =\frac{22}{110} =\frac{1}{5}$$​​

Tank will be filled by both P and Q working together = $$\frac{total\ work }{work\ done\ in\ 1\ minute}=\frac{1}{\frac{1}{5}}= 5 minutes$$  

Alternate Solution:

As per question:
P works 21
Q works 1
​Q can fill a cistern in 110 minutes
​Total work = 22
​both fill pipes are opened together = $$\frac{110}{22}$$​ = 5 min.​