If A can complete a work in 18 days and B can complete it in 27 days, how long w

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Question: If A can complete a work in 18 days and B can complete it in 27 days, how long will it take for them to finish the work if A works for 6 days and then B works for 6 days?

Options:

10 days
12 days
14 days
16 days

Correct Answer: 12 days

Solution:

A\'s work in 6 days = 6/18 = 1/3. Remaining work = 2/3. B\'s rate = 1/27. B will take 50/9 days to finish the remaining work.

If A can complete a work in 18 days and B can complete it in 27 days, how long w

Practice Questions

If A can complete a work in 18 days and B can complete it in 27 days, how long will it take for them to finish the work if A works for 6 days and then B works for 6 days?

10 days
12 days
14 days
16 days

Questions & Step-by-Step Solutions

If A can complete a work in 18 days and B can complete it in 27 days, how long will it take for them to finish the work if A works for 6 days and then B works for 6 days?

Step 1: Determine how much work A can do in one day. A can complete the work in 18 days, so A's work rate is 1/18 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 27 days, so B's work rate is 1/27 of the work per day.
Step 3: Calculate how much work A can do in 6 days. A's work in 6 days = 6 * (1/18) = 6/18 = 1/3 of the work.
Step 4: Calculate the remaining work after A works for 6 days. Remaining work = 1 - 1/3 = 2/3 of the work.
Step 5: Determine how long it will take B to finish the remaining work. B's rate is 1/27, so to find the time B needs to finish 2/3 of the work, use the formula: time = work / rate.
Step 6: Calculate the time B needs: time = (2/3) / (1/27) = (2/3) * (27/1) = 54/3 = 18 days.
Step 7: Add the time A worked and the time B worked to find the total time taken. Total time = 6 days (A) + 18 days (B) = 24 days.

Work Rate Calculation – Understanding how to calculate the amount of work done by individuals based on their rates and the time they work.
Combined Work – Analyzing how two individuals can work together and the impact of their individual contributions over time.
Fractional Work Remaining – Determining the remaining work after a certain amount of work has been completed.

If A can complete a work in 18 days and B can complete it in 27 days, how long w

What’s inside this PDF?

If A can complete a work in 18 days and B can complete it in 27 days, how long w

Practice Questions

Questions & Step-by-Step Solutions

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