Select the correct answerA can complete a work in 12 days, B in 15 days. When A and B worked alternatively, when started byOptions13 2/5 days12 2/5 days11 2/5 days13 3/5 days

To solve this problem, we first need to find out how much work A and B can do in one day.

1. A can complete the work in 12 days, so A can do 1/12 of the work in one day.
2. B can complete the work in 15 days, so B can do 1/15 of the work in one day.

When A and B work alternatively, they can complete (1/12 + 1/15) of the work in two days.

To simplify this, we find the least common multiple of 12 and 15, which is 60. So, A can do 5/60 of the work in one day and B can do 4/60 of the work in one day.

Therefore, in two days, A and B can complete (5/60 + 4/60) * 2 = 18/60 = 3/10 of the work.

To find out how many two-day periods it takes for A and B to complete the work, we divide the total work (1) by the work they can do in two days (3/10), which gives us 10/3 ≈ 3.33 two-day periods.

Since each two-day period is actually two days, we multiply 3.33 by 2 to find out how many days it takes for A and B to complete the work, which gives us 6.67 days.

However, since A and B work alternatively and A starts the work, A will work on the first day, B on the second day, A on the third day, B on the fourth day, A on the fifth day, B on the sixth day, and A will need to work on the seventh day to complete the work.

So, the correct answer is 6 full days and 2/5 of the seventh day, which is 6 2/5 days. But this option is not available in the given options.

Therefore, there seems to be a mistake in the question or the options provided.