A and B can together complete a task in 40 days. They worked together for 30 days and then B left. A finished the remaining task in next 22 days. In how many days A alone can finish the task?
- A48 days
- B88 days
- C30 days
- D40 days
Solution & Step-by-step Explanation
Let the total work be 40 units (since A and B together can complete it in 40 days).
Therefore, the combined efficiency of (A+B)=
40
40
=1 unit/day.
They worked together for 30 days:
Work completed in 30 days=1×30=30 units
Remaining work=40−30=10 units
A finishes this remaining 10 units of work in 22 days.
Efficiency of A=
Time taken
Remaining Work
=
22
10
=
11
5
units/day
The total days A alone will take to finish the total work of 40 units:
Time taken by A=
Efficiency of A
Total Work
=
11
5
40
=
5
40×11
=8×11=88 days
Therefore, the combined efficiency of (A+B)=
40
40
=1 unit/day.
They worked together for 30 days:
Work completed in 30 days=1×30=30 units
Remaining work=40−30=10 units
A finishes this remaining 10 units of work in 22 days.
Efficiency of A=
Time taken
Remaining Work
=
22
10
=
11
5
units/day
The total days A alone will take to finish the total work of 40 units:
Time taken by A=
Efficiency of A
Total Work
=
11
5
40
=
5
40×11
=8×11=88 days