# Shortcut Formulas for Time and Work Problems with examples

This time we are giving you Time and Work problems most commonly asked questions shortcut trick.

Formulas
If a person can do a piece of work in x days, then the work done by that person in one person
is 1/x.
And
If the work done by a person in one day is 1/x then he will complete the work in x days.
If A and B do a work in different amounts of time, then
A’s work: B’s work = time taken by B : time taken by A
If the efficiency of A is x times to that of B, then time taken by A is 1/x times to that of B.
If A and B can do a work in x days and A alone can do that work in y days, then B can do that work in
=xy/(y-x) days
If A can do a type of work in x days and B can do that work in y days, then both will complete the work together in
=xy/(x+y)            days

Below are More Shortcut Formulas for Time and Work Problems

If A, B and C can do a work in x, y and z days respectively, then all of them together will complete that work in                   xyz/(xy+yz+zx) days
If A and B can do a work in x days, B and C can do a work in y days and C and A can do that same work in z days, then all of them working together will complete the work in
2xyz/(xy+yz+zx)

If A can do a work in x days and B can do that work in y days. A and B, they started that work together but A left n days before the completion of the work and B alone have to complete the work. Then B will complete that work in
y(x+n)/(x+y) days
if A can do  a work in x days, B can do that work in y days and C can do that work in z days. All of them started the work together but A left after n days before the completion of the work. So B and C together will complete  the remaining work in
yz(n+x)/(xy+yz+zx) days

example:
Ram and Shyam can do a piece of work in 10 days and 20 days respectively. Both of them started the work together but Ram left after 5 days before the completion of the work. So in how many days  will the work be completed?
Solution:
Here  x= 10 days
And        y= 20 days
And        n= 5 days
So putting the formula of determining the time taken given above to complete the work:
=y(x+n)/(x+y)
=20(10+5)/(10+20)
= 10 days

Example 2:
If  A can complete a work in 10 days and B can complete that same work in 15 days, then, in how many days both of them together can complete the same work.
So putting the formula for above type of question, x=10, y= 15
here, = xy/ x+ y = 10 × 15/ (10+15) = 150/25= 6 days. Ans.

The work will be completed in 6 days.
So you just have to put the formula and you will get the answer.