A completes a work in 3 days while B completes it in 6 days. If they work alternately with A starting work first, then in how many days will the work be finished?
- A6
- B7
- C5
- D4
Solution & Step-by-step Explanation
Let the total work be the LCM of 3 and 6, which is 6 units.
Efficiency of A =
3
6
=2 units/day
Efficiency of B =
6
6
=1 unit/day
They work alternately starting with A:
Day 1: A works and completes 2 units.
Day 2: B works and completes 1 unit.
Total work completed in 2 days =2+1=3 units.
In the next 2 days (Day 3 and Day 4), they will complete another 3 units.
Total work completed in 4 days =3+3=6 units.
Since the total work is 6 units, it will be completely finished in exactly 4 days.
Efficiency of A =
3
6
=2 units/day
Efficiency of B =
6
6
=1 unit/day
They work alternately starting with A:
Day 1: A works and completes 2 units.
Day 2: B works and completes 1 unit.
Total work completed in 2 days =2+1=3 units.
In the next 2 days (Day 3 and Day 4), they will complete another 3 units.
Total work completed in 4 days =3+3=6 units.
Since the total work is 6 units, it will be completely finished in exactly 4 days.