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.