A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac

The question plays on the concept that time taken to do a work is inversely proportional to the rate of doing the work. We can deduce this relation from the expression

Work = Rate * Time i.e. Time = Work/Rate.

If the work done by two entities are the same, the ratio of time taken by them would be the inverse ratio of their rate of doing work.

Given:
The question gives us the relation between the rates of the wide and narrow pipes and asks us to find the ratio of time taken by all pipes working together to that of only wide pipes working together for filling up the tank.

Approach
The work done by all pipes working together and only wide pipes working together is the same i.e. filling the tank. As the work to be done is same, the ratio of time taken will be inversely proportional to the rate.So, inverting the ratio of rates would gives us the ratio of time. Let's see what information has been given to us about the rates of the pipes.

Working Out:
We are told that rate of work done by wide pipe is double the rate of work done by narrow pipe. If we assume the rate of narrow pipe to be r, the rate of wider pipe would be 2r.

We are asked to find (Time taken by all the pipes)/(Time taken by two wide pipes) = (Rate of two wide pipes)/ (Rate of all the pipes)=\(\frac{( 2r + 2r)}{( r +r + r +2r +2r)} = \frac{4}{7}\) which is our answer.

Takeaway
For time and work question, remember the relation between the work, time and rate for a set of different entities:

a. Greater the rate of doing work, lesser the amount of time taken, assuming the work done to be constant
b. Greater the amount of time taken, lesser the rate of doing work, assuming the work done to be constant
c. Greater the amount of time taken, greater the amount of work done, assuming the rate to be constant
d. Greater the rate of doing work, greater the amount of work done, assuming time taken to be constant

Regards
Harsh