A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in

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12 days

13 days

327 days

None of these

answer is D.

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Detailed Solution

Concept: We’ll convert the number of days in the units of work by writing it in the fractional form. Both the people work alternatively, we have calculated the number of works done in pairs. For the remaining work we will calculate by subtracting the obtained work from 1.
Let’s
A’s one day work = 116units
B’s one day work = 1 12units
Both are working on alternate days so; their 2 days’ work can be calculated as:
116+112=748
Thus, 1-pair of work done that is 748 units.
Now, Work done in 6 pairs=6×748
Work done in 6 pairs=4248
Thus, the number of units obtained has been the work done in 12 days.
Now,
Remaining work = 1- 4248
Remaining work=648
Now, we will find the work done on the 13th day as it’s A’s turn and A does 116 of the whole work in 1 day.
Thus, the remaining work is 48116=3units
Now, we will find the number of days 3 units work will take.
As B comes the next day, on the 14th day, Number of units of work=11248
Number of units of work=4 units
As only 3 units of work is required to be completed on the 14th day and B will take 34 of the day to complete the 3 remaining units of work.
Total days the work takes to get completed=12+1+34
Total days the work takes to get completed=1334
Hence, the correct option is 4.

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