TIME AND WORK

1. If A can do a piece of work in n days, then A's 1 day's work = (1/n).
2. If A’s 1 day's work = (1/n),then A can finish the work in n days.
3. A is thrice as good a workman as B, then:
1. Ratio of work done by A and B = 3 : 1.
2. Ratio of times taken by A and B to finish a work = 1 : 3.

Ex. 1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?
Sol. A’s 1 hour's work = 1/8
           B's 1 hour's work = 1/10

          (A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.

Ex. 2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?

Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).

       B's 1 day's work =((1/4)-(1/12))=(1/6)
       
     Hence, B alone can complete the work in 6 days.