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A and B can complete a work in 12 days and 18 days respectively. If they work to

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Question: A and B can complete a work in 12 days and 18 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. 12 days

Correct Answer: 8 days

Solution: 

A\'s work rate = 1/12, B\'s work rate = 1/18. Together, they work at (1/12 + 1/18) = 5/36. Time taken = 36/5 = 7.2 days.

A and B can complete a work in 12 days and 18 days respectively. If they work to

Practice Questions

Q1
A and B can complete a work in 12 days and 18 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. 12 days

Questions & Step-by-Step Solutions

A and B can complete a work in 12 days and 18 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 18 days, so B's work rate is 1/18 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 + 1/18).
  • Step 4: To add the fractions, find a common denominator. The least common multiple of 12 and 18 is 36.
  • Step 5: Convert A's work rate to have a denominator of 36: 1/12 = 3/36.
  • Step 6: Convert B's work rate to have a denominator of 36: 1/18 = 2/36.
  • Step 7: Now add the two rates: (3/36 + 2/36) = 5/36.
  • Step 8: The combined work rate of A and B is 5/36 of the work per day.
  • Step 9: To find out how long it takes them to complete the work together, take the reciprocal of their combined work rate: 1 / (5/36) = 36/5 days.
  • Step 10: Calculate 36/5 to get the final answer: 36/5 = 7.2 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 – Calculating the time taken to complete a task based on the combined work rate.
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