A and B complete a work in 12 and 15 days, respectively. They started the work alternatively for 1 day each and A started the work first. In how much time will 60% of the work be completed?
- A9 days
- B10 days
- C7 days
- D8 days
Solution & Step-by-step Explanation
Let the total work be the LCM of 12 and 15, which is 60 units.
Efficiency of A =
12
60
=5 units/day
Efficiency of B =
15
60
=4 units/day
We need to find the time taken to complete 60% of the work:
Target work=60% of 60=0.60×60=36 units
They work on alternate days starting with A:
Day 1 (A): 5 units
Day 2 (B): 4 units
In a 2-day cycle, the total work done is:
5+4=9 units
To complete 36 units:
Number of cycles=
9
36
=4 cycles
Since each cycle consists of 2 days:
Total time=4×2=8 days
Efficiency of A =
12
60
=5 units/day
Efficiency of B =
15
60
=4 units/day
We need to find the time taken to complete 60% of the work:
Target work=60% of 60=0.60×60=36 units
They work on alternate days starting with A:
Day 1 (A): 5 units
Day 2 (B): 4 units
In a 2-day cycle, the total work done is:
5+4=9 units
To complete 36 units:
Number of cycles=
9
36
=4 cycles
Since each cycle consists of 2 days:
Total time=4×2=8 days