Rules for Solving the Problems based on Time and Work

1) If a person can complete a work in  $\displaystyle n$ days, then in  $\displaystyle 1$ day he does   $\displaystyle n^{th}$of the work. We have

$\displaystyle \text{A Person's 1 Day Work} = \frac{1}{\text{Total number of days to complete the work}}$

2) If a person completes of a work in  $\displaystyle 1$ day, then he requires  $\displaystyle n$ number of days to complete the work

$\displaystyle \text{Total no. of days to complete the work} = \frac{1}{ \text{A Person's 1 Day Work}}$

3) If part of the work has been done and the remaining part of the work has to be done by a person A, then

$\displaystyle \text{No. of days to complete the work} = \frac{ \text{Remaining Part of the Work}}{ \text{A's 1 Day Work}}$

4) If  $\displaystyle \text{A is m}$  times as good ·a workman as  $\displaystyle B$ , then

1. i) Ratio of work done by  $\displaystyle A \text{ and } B$  in the same time  $\displaystyle = m : 1$
2. ii) Ratio of time taken by  $\displaystyle A \text{ and } B$  to finish the work  $\displaystyle =1: m$

5) If some persons work together to do a piece of work, then the money paid to them is divided among them in the ratio of their one day’s (or one hour’s) work.