Time and Work

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? (IGNOU, 2003)
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.

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?
(Bank P.O.2003)
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.

3. A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 bours each. How long will they take to do it, working together 8 hours a day?
A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)= 3 days

ans