A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone finish the whole work?Options2.5 days, 7.5 days5 days, 15 daysNone of these5 days, 8.5 days

This problem can be solved using the concept of work and efficiency in Time and Work.

Step 1: Understand the problem The problem states that A worked for 2 days and then B finished the work in 9 days. If A had worked for 3 days, B would have finished the work in 6 days. We need to find out how many days each of them would take to finish the work alone.

Step 2: Formulate the equations Let's assume the total work to be done is 1 unit. From the first condition, we can say that A's 2 days work + B's 9 days work = 1 unit of work. Let's denote A's 1 day work as 'a' and B's 1 day work as 'b'. So, we can write this equation as 2a + 9b = 1 ---- (Equation 1)

From the second condition, we can say that A's 3 days work + B's 6 days work = 1 unit of work. So, we can write this equation as 3a + 6b = 1 ---- (Equation 2)

Step 3: Solve the equations We can solve these two equations to find the values of 'a' and 'b'.

Subtract Equation 2 from Equation 1, we get: -1a + 3b = 0 => a = 3b ---- (Equation 3)

Substitute Equation 3 in Equation 1, we get: 2*(3b) + 9b = 1 => 6b + 9b = 1 => 15b = 1 => b = 1/15

Substitute b = 1/15 in Equation 3, we get: a = 3*(1/15) => a = 1/5

Step 4: Find the total time taken by A and B individually The total time taken by A to finish the work alone is 1/a = 1/(1/5) = 5 days The total time taken by B to finish the work alone is 1/b = 1/(1/15) = 15 days

So, the answer is 5 days and 15 days.