Two workers - Sagar and Manish - are working on a heavy machine to melt waste metal. Sagar can complete the work in 15 days while both workers on alternate basis can complete the work in 12 days. In how many days can Manish alone complete the work?
- A10
- B30
- C9
- D18
Solution & Step-by-step Explanation
When working on an alternate basis, they complete the work in 12 days. This means Sagar works for 6 days and Manish works for 6 days.
Let the total work be W.
Sagar's 1-day work rate is
15
W
.
In 6 days, the work completed by Sagar is:
Work by Sagar=6×
15
W
=
5
2W
The remaining work is completed by Manish in his 6 days of alternate work:
Remaining Work=W−
5
2W
=
5
3W
Therefore, Manish completes
5
3
of the total work in 6 days.
The time required for Manish alone to complete the entire work W is:
Total days for Manish=6×
3
5
=2×5=10 days
Let the total work be W.
Sagar's 1-day work rate is
15
W
.
In 6 days, the work completed by Sagar is:
Work by Sagar=6×
15
W
=
5
2W
The remaining work is completed by Manish in his 6 days of alternate work:
Remaining Work=W−
5
2W
=
5
3W
Therefore, Manish completes
5
3
of the total work in 6 days.
The time required for Manish alone to complete the entire work W is:
Total days for Manish=6×
3
5
=2×5=10 days