Correct Answer - Option 2 : 9 days
Given:
A can complete a piece of work in 10 days and B can complete it in 20 days.
A starts working and B works on every alternate day.
Before 5 days of the completion of work, B left the work.
Concepts used:
Efficiency = Work/Time
Calculation:
A can complete a piece of work in 10 days and B can complete it in 20 days.
Efficiency = Work/Time
1-day work of A = 1/10
1-day work of B = 1/20
1 day work of A and B = 1/10 + 1/20 = 3/20
A and B started working together but before 5 days of the completion of work, B left the work.
5 days work of A = 5/10 = 1/2
Remaining work = 1 – (1/2) = 1/2
A and B work together on every alternate day.
2 days work of A and B = 1-day work of A + 1-day work of A and B
⇒ 1/10 + 3/20
⇒ 5/20 = 1/4
1/4 work is done by A and B in 2 days.
⇒ 1 full piece of work is done by A and B in 8 days.
⇒ 1/2 work is done by A and B in 4 days.
Total time taken to complete work = 5 days + 4 days = 9 days.
∴ A and B complete piece of work in 9 days if B assists A on every alternate day and if B left work before 5 days of completion of work.
