Work and Time problems shortcuts

Basic point to remember while solving work and time problems

First of all work done in 1 day is calculated.If a person completes a work in x days,then Work done by that person in one day is 1/x.

Solving work and time problems-some useful tips

If the number of persons doing a piece of work is increased(or decreased) in a certain ratio,the time needed to do the same work will be decreased(increased) in the same ratio.
If the number of men do a certain work be changed in the ratio m:n, then the ratio of time taken to finish the work changes i the ratio n:m.
If A is twice as good as B, then A will take half the time taken by B to complete a certain piece of work.
If M1 persons can W1 works in D1 days and M2 persons can do W2 works in D2 days, then we relation between M1,W1,D1,M2,W2 and D2 is M1D1W2=M2D2W1
If a A can do X/Y of work in 1 hr,then he will take Y/X hrs to finish the work.

Shortcut formula for solving work and time problems

1.If A can do a work in x days and B can do the same work in y days,then A and B together can finish the work in

This is the first and foremost shortcut formula for solving work and time problems.For understanding better, derivation of this formula is given below.
Derivation of above formula:

Work done by A in one day=1/x
Work done by B in one day=1/y
Work done by A and B together in 1 day=1/x+1/y
Then total days taken to complete the work by A and B together=1/ Work done by A and B together in 1 day
=1/(1/x+1/y)
=1/((x+y)/xy))
=xy/(x+y)

2.If A can finish the work in x days ,B can finish the same work in y days and C finishes it in z days, then number of days taken to complete the work if all three work together is

3.If A&B together can finish the work in x days,B&C together finishes in y days and C&A together finishes in z days,then work done by A,B and C together in 1 day is

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