A started a work and left working after 9 days now B finished the remaining work in 24 days. Had A left the work after working for 13 days then B would have finished the remaining work in next 18 days. Then find in how many days A and B together can complete the work?Options12 days15 days16 days18 days

To solve this problem, we need to first understand the concept of work and time. The amount of work done by a person is inversely proportional to the time taken.

Step 1: Let's assume the total work to be done is 1 unit.

Step 2: From the problem, we know that A works for 9 days and B finishes the remaining work in 24 days. This means that the work done by A in 1 day + the work done by B in 1 day = 1/33 (since 9 days of A + 24 days of B = 33 days to complete 1 unit of work).

Step 3: Similarly, if A works for 13 days and B finishes the remaining work in 18 days, the work done by A in 1 day + the work done by B in 1 day = 1/31 (since 13 days of A + 18 days of B = 31 days to complete 1 unit of work).

Step 4: Now, we have two equations and two unknowns (the work done by A in 1 day and the work done by B in 1 day). We can solve these equations simultaneously to find the values.

Step 5: Subtracting the second equation from the first, we get the work done by A in 1 day = 1/33 - 1/31 = 2/ (33*31).

Step 6: Substituting this value in the first equation, we get the work done by B in 1 day = 1/33 - 2/(3331) = 1/(3331).

Step 7: Now, if A and B work together, the work done in 1 day = work done by A in 1 day + work done by B in 1 day = 2/(3331) + 1/(3331) = 3/(33*31).

Step 8: Therefore, the total time taken by A and B to complete the work together = 1 / (work done in 1 day) = 33*31/3 = 341 days.

However, this is not one of the options given. There might be a mistake in the problem or the options provided.