A and B together can do a specific work in 8 days. B alone can do it in 10 days, then time taken by A alone is?

Sure, let's solve this step by step:

Step 1: First, we need to find out how much work A and B can do in one day. Since they can complete the work in 8 days together, they can do 1/8 of the work in one day.

Step 2: Similarly, we find out how much work B can do in one day. Since B can complete the work in 10 days alone, B can do 1/10 of the work in one day.

Step 3: Now, to find out how much work A can do in one day, we subtract the work done by B in one day from the work done by A and B together in one day. So, A can do 1/8 - 1/10 of the work in one day.

Step 4: Simplify the above expression to find out the work done by A in one day. The least common multiple (LCM) of 8 and 10 is 40. So, A can do (5-4)/40 = 1/40 of the work in one day.

Step 5: Finally, to find out how many days A would take to complete the work alone, we take the reciprocal of the work A can do in one day. So, A would take 40 days to complete the work alone.