**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 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}

Example

**Rule 2:**

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

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

Example

**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

**Profit And Loss**

**Cost Price: **It is the price at which any article or unit or item is bought. It is abbreviated as CP.

**Selling Price: **It is the price at which any article or unit or item is sold. It is abbreviated as SP.

**Profit: **If Selling Price is greater than Cost Price then seller makes profit.

Profit = SP – CP

**Loss:** If Cost Price is greater than Selling Price then seller incurs loss.

Loss = CP – SP

**Basic Formulas:**

One point is to be noted that loss or profit is always calculated with reference to CP.