A alone can complete a work in 18 days and B alone in 14 days. Starting with A, they work on alternate days. The total work will be completed in:
- A14
9
7
days - B15
9
7
days - C16
9
7
days - D13
9
7
days
Solution & Step-by-step Explanation
Let the total work be the LCM of 18 and 14, which is 126 units.
Efficiency of A=
18
126
=7 units/day
Efficiency of B=
14
126
=9 units/day
They work on alternate days starting with A:
Day 1 (A): 7 units
Day 2 (B): 9 units
In a 2-day cycle, work completed = 7+9=16 units
Number of complete 2-day cycles needed to reach close to 126:
7×16=112 units
So, in 7×2=14 days, the work completed is 112 units.
Remaining work = 126−112=14 units
On the 15
th
day, it is A's turn:
A completes 7 units of work.
Remaining work after day 15 = 14−7=7 units
On the 16
th
day, it is B's turn:
B's efficiency is 9 units/day.
Time taken by B to finish the remaining 7 units =
9
7
day
Total time taken = 15+
9
7
=15
9
7
days
Efficiency of A=
18
126
=7 units/day
Efficiency of B=
14
126
=9 units/day
They work on alternate days starting with A:
Day 1 (A): 7 units
Day 2 (B): 9 units
In a 2-day cycle, work completed = 7+9=16 units
Number of complete 2-day cycles needed to reach close to 126:
7×16=112 units
So, in 7×2=14 days, the work completed is 112 units.
Remaining work = 126−112=14 units
On the 15
th
day, it is A's turn:
A completes 7 units of work.
Remaining work after day 15 = 14−7=7 units
On the 16
th
day, it is B's turn:
B's efficiency is 9 units/day.
Time taken by B to finish the remaining 7 units =
9
7
day
Total time taken = 15+
9
7
=15
9
7
days