A can do a work in 8 days and B can do the same work in 12 days. If they work on it for 3 days, then what fraction of the work is left?
- A24
19
- B8
5
- C20
17
- D8
3
Solution & Step-by-step Explanation
Let the total work be the LCM of 8 and 12, which is 24 units.
Efficiency of A =
8
24
=3 units/day
Efficiency of B =
12
24
=2 units/day
Combined efficiency of A and B = 3+2=5 units/day
Work completed by both in 3 days = 5×3=15 units
Remaining work = Total work−Completed work=24−15=9 units
Fraction of work left =
Total work
Remaining work
=
24
9
=
8
3
Efficiency of A =
8
24
=3 units/day
Efficiency of B =
12
24
=2 units/day
Combined efficiency of A and B = 3+2=5 units/day
Work completed by both in 3 days = 5×3=15 units
Remaining work = Total work−Completed work=24−15=9 units
Fraction of work left =
Total work
Remaining work
=
24
9
=
8
3