**Time and Work Formula**

**If A can do a piece of work in n days, then A’s 1-day work is= 1/n**

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

**If A is thrice as good a workman as B, then-**

The ratio of work done by A and B = **3:1**

The ratio of time taken by A and B to finish work = **1:3**

**If M _{1} men can do a W_{1} piece of work, working T_{1} hours daily in D_{1} days and M_{2} men can complete W_{2} work, working T_{2} hours in D_{2} days then-**

**M _{1 }D_{1 }T_{1 }W_{2} = M_{2 }D_{2 }T_{2 }W_{1}**

**If A completes a piece of work alone in x days and B completes the same work in y days. Then they together will finish the work in–**

**(x × y/x+y) days**

**If ‘A’ and ‘B’ completes a piece of work together in x days and B alone completes the same work in y days. Then ‘A’ alone will finish the work in-**

**(x – y/y – x) days**

**If three men A, B, and C alone finish a piece of work in x, y, and z days. Then they together finish the work in-**

**( xyz/xy + yz + zx ) days**

**EXAMPLE-**

**1. P can do a work in 10 days and Q in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is?**

**Solution-**

P’s 1 day’s work = 1/10

Q’s 1 day’s work = 1/20

(P + Q)’s 1 day’s work = \frac { 1 }{ 10 } +\frac { 1 }{ 20 } = 3/20

(P + Q)’s 5 day’s work = 5\times \frac { 3 }{ 20 } =\frac { 3 }{ 4 }

So, now the Remaining work is = 1 – (3/4) = 1/4 (Answer)