A does 75% of a work in 45 days. He then calls in B and they together finish the remaining work in 5 days. How long B alone would take to do the whole work?
- A15 days
- B45 days
- C60 days
- D30 days
Solution & Step-by-step Explanation
A completes 75% (
4
3
) of the work in 45 days.
Time taken by A to complete the whole work alone = 45×
3
4
=60 days.
So, A's 1-day work rate =
60
1
.
Remaining work = 100%−75%=25% (
4
1
).
A and B together complete this remaining
4
1
work in 5 days.
Time taken by A and B together to do the whole work = 5×4=20 days.
So, (A + B)'s 1-day work rate =
20
1
.
B's 1-day work rate = (A + B)'s 1-day rate - A's 1-day rate
B’s 1-day rate=
20
1
−
60
1
=
60
3−1
=
60
2
=
30
1
Therefore, B alone can complete the work in 30 days.
4
3
) of the work in 45 days.
Time taken by A to complete the whole work alone = 45×
3
4
=60 days.
So, A's 1-day work rate =
60
1
.
Remaining work = 100%−75%=25% (
4
1
).
A and B together complete this remaining
4
1
work in 5 days.
Time taken by A and B together to do the whole work = 5×4=20 days.
So, (A + B)'s 1-day work rate =
20
1
.
B's 1-day work rate = (A + B)'s 1-day rate - A's 1-day rate
B’s 1-day rate=
20
1
−
60
1
=
60
3−1
=
60
2
=
30
1
Therefore, B alone can complete the work in 30 days.