Working separately, A and B can complete a work in 15 days and 18 days, respectively. If A starts the work and they work on alternate days, one on each day, then in how many days will the work be completed?
- A17
3
1
days - B16
3
1
days - C18
3
2
days - D15
3
2
days
Solution & Step-by-step Explanation
Time taken by A=15 days
Time taken by B=18 days
Let the total work be the LCM of 15 and 18, which is 90 units.
Efficiency of A=
15
90
=6 units/day
Efficiency of B=
18
90
=5 units/day
Since they work on alternate days starting with A:
Day 1 (A) = 6 units
Day 2 (B) = 5 units
Work done in a 2-day cycle = 6+5=11 units
Number of complete 2-day cycles to get close to 90 units:
90÷11=8 cycles with a remainder of 2 units
Work done in 8 cycles (16 days) = 8×11=88 units
Remaining work = 90−88=2 units
On the 17th day, it is A's turn.
Time taken by A to complete the remaining 2 units =
Efficiency of A
Remaining Work
=
6
2
=
3
1
day
Total time taken = 16+
3
1
=16
3
1
days
Time taken by B=18 days
Let the total work be the LCM of 15 and 18, which is 90 units.
Efficiency of A=
15
90
=6 units/day
Efficiency of B=
18
90
=5 units/day
Since they work on alternate days starting with A:
Day 1 (A) = 6 units
Day 2 (B) = 5 units
Work done in a 2-day cycle = 6+5=11 units
Number of complete 2-day cycles to get close to 90 units:
90÷11=8 cycles with a remainder of 2 units
Work done in 8 cycles (16 days) = 8×11=88 units
Remaining work = 90−88=2 units
On the 17th day, it is A's turn.
Time taken by A to complete the remaining 2 units =
Efficiency of A
Remaining Work
=
6
2
=
3
1
day
Total time taken = 16+
3
1
=16
3
1
days