Correct Answer - Option 1 : 28/3 days
Given:
A piece of job is completed by A and B together in 5 days.
A works alone for 6 days and leaves after completing three-fourth of the work.
B alone completes the remaining work.
Concepts used:
Time = Work/Efficiency
1 day work of individual = Work/Time
Calculation:
¾ of the total work is done by A in 6 days.
⇒ Efficiency of A = 3/4/6
⇒ Efficiency of A = 1/8
⇒ A alone can compete the work in 8 days.
Let B alone complete the work in x days.
⇒ (1/8) + (1/x) = 1/5
⇒ 1/x = (1/5) – (1/8)
⇒ 1/x = 3/40
⇒ x = 40/3 days
Remaining work after A left = 1 – (3/4) = ¼
¼ work is done by B alone.
Time taken by B to complete one-fourth of the work = (1/4)/(3/40) = 10/3 days
Total time taken by A and B in completing work = 6 + (10/3) = 28/3 days
∴ Total work gets completed in 28/3 days.
