To solve this problem, we need to first understand the concept of work and time. The rate of work done is inversely proportional to the time taken to complete the work.

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

Step 2: According to the problem, A and B together can do this work in 12 days. So, their combined rate of work is 1/12 work/day.

Step 3: Similarly, B and C together can do this work in 16 days. So, their combined rate of work is 1/16 work/day.

Step 4: Now, it's given that A works for 5 days, B works for 7 days and C completes the remaining work in 13 days. This means that the total work done by A, B and C is equal to 1 unit.

So, we can write the equation as: 5A + 7B + 13C = 1

Step 5: We also know that A + B = 1/12 and B + C = 1/16.

Step 6: Subtracting these two equations, we get A - C = 1/12 - 1/16 = 1/48.

Step 7: Substituting A - C = 1/48 in the equation 5A + 7B + 13C = 1, we get 5(1/48 + C) + 7B = 1.

Step 8: Solving this equation, we get B = 1/24.

So, B alone can do the work in 24 days. Therefore, the correct answer is 24 days.

Question

To solve this problem, we need to first understand the concept of work and time. The rate of work done is inversely proportional to the time taken to complete the work.

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

Step 2: According to the problem, A and B together can do this work in 12 days. So, their combined rate of work is 1/12 work/day.

Step 3: Similarly, B and C together can do this work in 16 days. So, their combined rate of work is 1/16 work/day.

Step 4: Now, it's given that A works for 5 days, B works for 7 days and C completes the remaining work in 13 days. This means that the total work done by A, B and C is equal to 1 unit.

So, we can write the equation as: 5A + 7B + 13C = 1

Step 5: We also know that A + B = 1/12 and B + C = 1/16.

Step 6: Subtracting these two equations, we get A - C = 1/12 - 1/16 = 1/48.

Step 7: Substituting A - C = 1/48 in the equation 5A + 7B + 13C = 1, we get 5(1/48 + C) + 7B = 1.

Step 8: Solving this equation, we get B = 1/24.

So, B alone can do the work in 24 days. Therefore, the correct answer is 24 days.

Knowee AI · Accepted Answer

To solve this problem, we need to first understand the concept of work and time. The rate of work done is inversely proportional to the time taken to complete the work.

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

Step 2: According to the problem, A and B together can do this work in 12 days. So, their combined rate of work is 1/12 work/day.

Step 3: Similarly, B and C together can do this work in 16 days. So, their combined rate of work is 1/16 work/day.

Step 4: Now, it's given that A works for 5 days, B works for 7 days and C completes the remaining work in 13 days. This means that the total work done by A, B and C is equal to 1 unit.

So, we can write the equation as: 5A + 7B + 13C = 1

Step 5: We also know that A + B = 1/12 and B + C = 1/16.

Step 6: Subtracting these two equations, we get A - C = 1/12 - 1/16 = 1/48.

Step 7: Substituting A - C = 1/48 in the equation 5A + 7B + 13C = 1, we get 5(1/48 + C) + 7B = 1.

Step 8: Solving this equation, we get B = 1/24.

So, B alone can do the work in 24 days. Therefore, the correct answer is 24 days.

Select the correct answerA and B together can do a piece of work in 12 days which B and C together do in 16 days. If A works for 5 days, B works for 7 days than C completes the remaining work in 13 days. In how much time B alone does the whole work?Options48 days16 days24 days12 days

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