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A and B can complete a work in 12 days and 15 days respectively. If they work to

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Question: A and B can complete a work in 12 days and 15 days respectively. If they work together, how long will it take them to complete the work?

Options:

  1. 6 days
  2. 8 days
  3. 10 days
  4. 5 days

Correct Answer: 8 days

Solution: 

A\'s work rate = 1/12, B\'s work rate = 1/15. Combined rate = 1/12 + 1/15 = 5/60 = 1/12. Time taken = 12 days.

A and B can complete a work in 12 days and 15 days respectively. If they work to

Practice Questions

Q1
A and B can complete a work in 12 days and 15 days respectively. If they work together, how long will it take them to complete the work?
  1. 6 days
  2. 8 days
  3. 10 days
  4. 5 days

Questions & Step-by-Step Solutions

A and B can complete a work in 12 days and 15 days respectively. If they work together, how long will it take them to complete the work?
  • Step 1: Determine A's work rate. A can complete the work in 12 days, so A's work rate is 1/12 of the work per day.
  • Step 2: Determine B's work rate. B can complete the work in 15 days, so B's work rate is 1/15 of the work per day.
  • Step 3: Add A's and B's work rates together to find their combined work rate. This is done by calculating 1/12 + 1/15.
  • Step 4: To add the fractions, find a common denominator. The least common multiple of 12 and 15 is 60.
  • Step 5: Convert A's work rate to the common denominator: 1/12 = 5/60.
  • Step 6: Convert B's work rate to the common denominator: 1/15 = 4/60.
  • Step 7: Now add the two rates: 5/60 + 4/60 = 9/60.
  • Step 8: Simplify the combined work rate: 9/60 = 3/20.
  • Step 9: The combined work rate of A and B is 3/20 of the work per day.
  • Step 10: To find out how long it takes them to complete the work together, take the reciprocal of their combined work rate: 1 / (3/20) = 20/3 days.
  • Step 11: Convert 20/3 days into a more understandable format: 20/3 days is approximately 6.67 days.
  • Work Rate – Understanding how to calculate individual work rates and combine them to find the total work rate when multiple workers are involved.
  • Fraction Addition – Adding fractions with different denominators to find a common work rate.
  • Time Calculation – Using the combined work rate to determine the total time taken to complete a task.
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