A and B can complete a task in 40 days and 16 days respectively. A started the task alone and then after 12 days B joined him till the completion of the task. How long did the task last after B joined the task?
- A8 days
- B6 days
- C14 days
- D12 days
Solution & Step-by-step Explanation
Let the total work be the LCM of 40 and 16, which is 80 units.
Efficiency of A=
40
80
=2 units/day
Efficiency of B=
16
80
=5 units/day
A worked alone for 12 days:
Work done by A in 12 days=2×12=24 units
Remaining work=80−24=56 units
Now B joins A, so their combined efficiency is:
Combined efficiency=2+5=7 units/day
The time taken by both to complete the remaining work after B joined:
Time=
Combined efficiency
Remaining work
=
7
56
=8 days
Efficiency of A=
40
80
=2 units/day
Efficiency of B=
16
80
=5 units/day
A worked alone for 12 days:
Work done by A in 12 days=2×12=24 units
Remaining work=80−24=56 units
Now B joins A, so their combined efficiency is:
Combined efficiency=2+5=7 units/day
The time taken by both to complete the remaining work after B joined:
Time=
Combined efficiency
Remaining work
=
7
56
=8 days