A can complete a work in 12 days, B in 15 days. When A and B worked alternatively, when started byOptions12 2/5 days13 2/5 days11 2/5 days13 3/5 days

The question seems to be asking how long it would take for A and B to complete a task if they worked on it alternately, starting with A. Here's how you can solve it:

Step 1: Determine how much of the work each person can do in a day. A can complete the work in 12 days, so A can do 1/12 of the work in a day. B can complete the work in 15 days, so B can do 1/15 of the work in a day.

Step 2: Determine how much work is done when A and B work alternately for two days (one day each). In two days, A and B together can do (1/12 + 1/15) of the work. This equals 27/180 or 3/20 of the work.

Step 3: Determine how many two-day periods it takes for A and B to complete the work. Since they can do 3/20 of the work in two days, it would take them (20/3) two-day periods to complete the work. This is approximately 6.67 two-day periods.

Step 4: Since they can't work a fraction of a day, round up to the nearest whole number of two-day periods. This gives 7 two-day periods, or 14 days.

Step 5: However, since A starts the work, on the 14th day, A will be working and will finish the work before B starts. So, we need to subtract the work that A does on the 14th day. A does 1/12 of the work in a day, so subtracting this from the 14 days gives 14 - (1/12) = 13 11/12 days.

So, the closest answer to this is 13 2/5 days.