If A can complete a work in 12 days and B can complete it in 16 days, how long w

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Question: If A can complete a work in 12 days and B can complete it in 16 days, how long will it take for A and B to finish the work if they work together for 4 days?

Options:

2 days
3 days
4 days
5 days

Correct Answer: 4 days

Solution:

Combined rate = (1/12 + 1/16) = 7/48. In 4 days, they complete 28/48 = 7/12 of the work. Remaining work = 5/12, which will take 5/7 days.

If A can complete a work in 12 days and B can complete it in 16 days, how long w

Practice Questions

If A can complete a work in 12 days and B can complete it in 16 days, how long will it take for A and B to finish the work if they work together for 4 days?

2 days
3 days
4 days
5 days

Questions & Step-by-Step Solutions

If A can complete a work in 12 days and B can complete it in 16 days, how long will it take for A and B to finish the work if they work together for 4 days?

Step 1: Determine how much work A can do in one day. A can complete the work in 12 days, so A's work rate is 1/12 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 16 days, so B's work rate is 1/16 of the work per day.
Step 3: Calculate the combined work rate of A and B when they work together. Add A's rate (1/12) and B's rate (1/16).
Step 4: To add the fractions, find a common denominator. The least common multiple of 12 and 16 is 48. Convert the rates: A's rate becomes 4/48 and B's rate becomes 3/48.
Step 5: Add the converted rates: (4/48) + (3/48) = 7/48. This means together they can complete 7/48 of the work in one day.
Step 6: Calculate how much work A and B can complete in 4 days. Multiply their combined rate (7/48) by 4 days: (7/48) * 4 = 28/48.
Step 7: Simplify 28/48 to 7/12. This means A and B together complete 7/12 of the work in 4 days.
Step 8: Determine the remaining work. Subtract the completed work (7/12) from the total work (1): 1 - 7/12 = 5/12.
Step 9: Calculate how long it will take A and B to finish the remaining work (5/12). Use their combined rate (7/48) to find the time: Time = Remaining work / Combined rate = (5/12) / (7/48).
Step 10: To divide the fractions, multiply by the reciprocal: (5/12) * (48/7) = 5 * 4 / 7 = 20/7 days.

Work Rate – Understanding how to calculate the combined work rate of two individuals and how to determine the amount of work completed over a period.
Fractional Work – Using fractions to represent parts of work completed and remaining work.
Time Calculation – Calculating the time required to complete the remaining work based on the combined work rate.

If A can complete a work in 12 days and B can complete it in 16 days, how long w

What’s inside this PDF?

If A can complete a work in 12 days and B can complete it in 16 days, how long w

Practice Questions

Questions & Step-by-Step Solutions

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