Time & Work

In finding out the solution of the problems on time and work, it is necessary to determine the work done in a unit time. This unit time is generally taken as an hour or a minute or a day.

General rules:
If a man can do a piece of work in 10 days, he will finish 1/10 of it in 1 day.
If a man can do 1/8 of a work in an hour, he will complete the whole work in 8 hours.
If Parul can do 1/10 of a work in 1 day and his sister does 1/5 of the same work in 1 day, then both together can do work in a day.
If A is thrice as good a workman as B, then A's work: B's work = 3 : 1 and time taken by A : time taken by B = 1 : 3 for a certain piece of work.

Also remember:
If A can do a piece of work in 'n' days, work done by A in 1 day = '1/n'.
If A does '1/n' work in a day, A can finish the work in 'n' days.
If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then M1 D1 H1/W1 = M2 D2 H2/W2
If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq/(p+q) days.
If A is thrice as good as B in work, then Ratio of work done by A and B = 3 : 1 Ratio of time taken to finish a work by A and B = 1 : 3.

Example: A can do a piece of work in 6 days and B alone can do it in 8 days. How long would it take for both of them to finish.

A's one day's work = B's one day's work = (A + B)'s one day's work = + = ?1 work is done in days

Example: A and B can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone do it?
(A + B)'s one day's work = ; A's one day's work =
? B's one day's work = - = ; ? B can complete that work alone in 15 days.

Example: A and B can do a piece of work in 40days. B and Can do a piece of work in30 days. C and A can do a piece of work in 24 days. How long would they all take to do the same work?

? 2(A + B + C)'s one day's work
= =
? (A + B + C)'s one day's work =
? (A + B + C) together can complete the work in 20 days.