# Time and Work Shortcut Methods

Time and Work problems are most frequently asked problems in quantitative aptitude. To solve these problems very quickly, you should understand the concept of Time and Work and some shortcut methods.

If a man can do a piece of work in 5 days, then he will finish 1/5th of the work in one day.

If a man can finish 1/5th of the work in one day then he will take 5 days to complete the work.

If a man can do 5/6th of work in one hour then he will take 6/5 hours to complete the full work.

If A works three times faster than B then A takes 1/3rd the time taken by B.

Here are some shortcut rules which can be very useful while solving Time and Work problems.

In total 9 rules are given here.

**Rule 1: Universal Rule**

This rule can be used in almost every problems.

If M_{1} persons can do W_{1} work in D_{1} days and M_{2} persons can do W_{2} works in D_{2} days then we can say

M_{1}D_{1}W_{2} = M_{2}D_{2}W_{1}

If the persons work T_{1} and T_{2} hours per day respectively then the equation gets modified to

M_{1}D_{1}T_{1}W_{2} = M_{2}D_{2}T_{2}W_{1}

If the persons has efficiency of E_{1} and E_{2} respectively then,

M_{1}D_{1}T_{1}E_{1}W_{2} = M_{2}D_{2}T_{2}E_{2}W_{1}

**5 men can prepare 10 cycles in 6 days working 6 hours a day. Then in how many days can 12 men prepare 16 cycles working 8 hours a day?**

**Sol:**

Here M_{1} = 5, W_{1} = 10, D_{1} = 6, T_{1} = 6 and

M_{2} = 1_{2}, W_{2} = 16, T_{2} = 8

So from the above rule

M_{1}D_{1}T_{1}W_{2} = M_{2}D_{2}T_{2}W_{1}

5 × 6 × 6 × 16 = 12 × D_{2} × 8 × 10

D_{2} = 3 Days.

So they will complete the work in 3 days.

**Rule 2:**

If A can do a piece of work in n days, then

The work done by A in one day = 1/n

If A can repair 50 cycles in 5 days then A can repair 50/5 = 10 cycles in one day.

**Rule 3:**

If A can do a work in D_{1} days and B can do the same work in D_{2} days then A and B together can do the same work

**If A can do a piece of work in 10 days and B can do the same work in 15 days then how long will they take if they both work together?**

**Sol:**

A can finish the work in D_{1} = 10 days.

B can finish the work in D_{2} = 15 days.