Time and Work

Work is the job or task completed (Distance) in a specified time. Time and Work are in direct proportion. If the amount of work increases, time to complete the work also increases.

Work as Man Days

If a man does a work in 10 days, total work does is 10 man days. Two men will take 5 days (10 man days). The work done by one man in one day is 1/10^th of total work.

Pipes and Cisterns

Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.
Outlet: A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.

1. If an inlet pipe can fill a cistern in A hours, the part filled in 1 hour = 1/A (same principle as time and work).
2. If pipe A is ‘x’ times bigger than pipe B, then pipe A will take 1/x^th (less time) of the time taken by pipe B to fill the cistern.
3. If an inlet pipe can fill a tank in A hours and an outlet pipe empties the full tank in B hours (B>A), then the net part filled in 1 hour when both the pipes are opened will be 1/A - 1/B.
4. If X and Y fill a cistern in m and n hours respectively, then together they will take (1/m + 1/n) hours to fill the cistern.
5. If an inlet pipe fills a cistern in a hours and takes x minutes longer to fill the cistern due to a leak in the cistern, then the time in which the leak will empty the cistern is given by a(1+a/x)

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