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If a man can complete a work in 10 days and another man can complete the same wo

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Question: If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?

Options:

  1. 6 days
  2. 8 days
  3. 10 days
  4. 12 days

Correct Answer: 6 days

Solution: 

Work done by first man in one day = 1/10. Work done by second man in one day = 1/15. Together they do = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.

If a man can complete a work in 10 days and another man can complete the same wo

Practice Questions

Q1
If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?
  1. 6 days
  2. 8 days
  3. 10 days
  4. 12 days

Questions & Step-by-Step Solutions

If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?
  • Step 1: Understand that the first man can complete the work in 10 days. This means he does 1/10 of the work in one day.
  • Step 2: Understand that the second man can complete the work in 15 days. This means he does 1/15 of the work in one day.
  • Step 3: To find out how much work they can do together in one day, add the work done by both men in one day: 1/10 + 1/15.
  • Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
  • Step 5: Convert 1/10 to a fraction with a denominator of 30: 1/10 = 3/30.
  • Step 6: Convert 1/15 to a fraction with a denominator of 30: 1/15 = 2/30.
  • Step 7: Now add the two fractions: 3/30 + 2/30 = 5/30.
  • Step 8: Simplify 5/30 to 1/6. This means together they can complete 1/6 of the work in one day.
  • Step 9: To find out how many days it takes for them to complete the entire work together, take the reciprocal of 1/6, which is 6.
  • Step 10: Therefore, it will take both men 6 days to complete the work together.
  • Work Rate – Understanding how to calculate the work done by individuals based on their rates of work.
  • Combined Work Rate – Calculating the total work rate when two or more individuals work together.
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