Time : Amount of days required to complete a job or work.

Work : Amount of job actually done.

If A can do a work in ‘n’ days, then amount of work done by A in 1 day :

[math]
\frac{1}{n}
[/math]

If A’s 1 day work = 1/n, then A can finish the work in ‘n’ days.

If workman A is twice as good as B, then

Ratio of work done by A & B = 2 : 1

Ratio of time taken by A and B to finish work = 1 : 2

Problem Type 1 :

If A can do work in X days and B can do same work in Y days. In how days they could complete it by working together.

For such problem remember,

A’s 1 day work : 1/X

B’s 1 day work : 1/Y

So, (A + B)’s one day work will be given as :

[math]
\boxed
{
\frac{1}{X}\;+\;\frac{1}{Y}
}
[/math]

Problem Type 2 :

If A and B together can complete a piece of work in Z days. If A alone can complete same work in X days, in how many days can B alone complete that work.

For such problem, remember :

(A+B)’s 1 day work : 1/Z

A’s 1 day work : 1/X

So, B’s 1 day work is given as :

[math]
\boxed
{
\frac{1}{Z}\;-\;\frac{1}{X}
}
[/math]