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A man can complete a work in 10 days. If he works for 3 days and then is joined

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Question: A man can complete a work in 10 days. If he works for 3 days and then is joined by another man who can complete the same work in 15 days, how many more days will they take to finish the work?

Options:

  1. 4
  2. 5
  3. 6
  4. 7

Correct Answer: 5

Solution: 

Work done by the first man in 3 days = 3/10. Remaining work = 1 - 3/10 = 7/10. Combined work rate = 1/10 + 1/15 = 1/6. Time to finish = (7/10) / (1/6) = 4.2 days.

A man can complete a work in 10 days. If he works for 3 days and then is joined

Practice Questions

Q1
A man can complete a work in 10 days. If he works for 3 days and then is joined by another man who can complete the same work in 15 days, how many more days will they take to finish the work?
  1. 4
  2. 5
  3. 6
  4. 7

Questions & Step-by-Step Solutions

A man can complete a work in 10 days. If he works for 3 days and then is joined by another man who can complete the same work in 15 days, how many more days will they take to finish the work?
  • Step 1: Determine how much work the first man can do in one day. Since he can complete the work in 10 days, his work rate is 1/10 of the work per day.
  • Step 2: Calculate how much work the first man does in 3 days. Multiply his daily work rate (1/10) by 3 days: (1/10) * 3 = 3/10.
  • Step 3: Find out how much work is left after the first man has worked for 3 days. The total work is 1, so remaining work = 1 - 3/10 = 7/10.
  • Step 4: Determine the work rate of the second man. He can complete the work in 15 days, so his work rate is 1/15 of the work per day.
  • Step 5: Calculate the combined work rate of both men when they work together. Add their work rates: (1/10) + (1/15). To add these fractions, find a common denominator, which is 30. So, (3/30) + (2/30) = 5/30 = 1/6.
  • Step 6: Now, find out how long it will take for both men to finish the remaining work of 7/10. Use the formula: time = work / rate. So, time = (7/10) / (1/6).
  • Step 7: To divide by a fraction, multiply by its reciprocal. So, (7/10) * (6/1) = 42/10 = 4.2 days.
  • Work Rate Calculation – Understanding how to calculate the work done by individuals based on their rates and the time they work.
  • Combined Work Rate – Calculating the combined work rate of two individuals working together.
  • Fractional Work Remaining – Determining the remaining work after a certain amount has been completed.
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