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 days16 days18 days15 days

This problem can be solved using the concept of work and time.

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 A's 9 days of work + B's 24 days of work = 1 unit of work.

Step 3: Similarly, if A works for 13 days and B finishes the remaining work in 18 days, this also equals 1 unit of work.

Step 4: From these two equations, we can set up a system to solve for A's and B's work rates.

Let's denote A's work rate as a and B's work rate as b.

From step 2, we have the equation 9a + 24b = 1. From step 3, we have the equation 13a + 18b = 1.

Step 5: Solve this system of equations to find the values of a and b.

Step 6: Once we have the work rates of A and B, we can find out how long they would take to complete the work together.

The total work rate when A and B work together is a + b.

Step 7: The time taken to complete the work is the total work divided by the total work rate, which is 1/(a+b).

Step 8: Calculate this value to find the answer.

This is the step-by-step process to solve this problem.

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

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 A's 9 days of work + B's 24 days of work = 1 unit of work.

Step 3: Similarly, if A works for 13 days and B finishes the remaining work in 18 days, this also equals 1 unit of work.

Step 4: From these two equations, we can form a system of linear equations to solve for A's and B's work rates (the amount of work they can do per day).

Let's denote A's work rate as a and B's work rate as b.

From step 2, we have the equation: 9a + 24b = 1 From step 3, we have the equation: 13a + 18b = 1

Step 5: Solve this system of equations to find the values of a and b.

Step 6: Once we have the work rates of A and B, we can find out how long it would take for A and B to complete the work together. This can be found by dividing the total work (1 unit) by the sum of their work rates (a + b).

The answer will be one of the options given.

No answer