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A and B can complete a work in 12 days and 15 days respectively. In how many day

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Question: A and B can complete a work in 12 days and 15 days respectively. In how many days can they complete the work together?

Options:

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

Correct Answer: 8

Solution: 

A\'s work rate = 1/12, B\'s work rate = 1/15. Together, they work at the rate of 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Therefore, they complete the work in 20/3 days = 6.67 days.

A and B can complete a work in 12 days and 15 days respectively. In how many day

Practice Questions

Q1
A and B can complete a work in 12 days and 15 days respectively. In how many days can they complete the work together?
  1. 6
  2. 8
  3. 10
  4. 5

Questions & Step-by-Step Solutions

A and B can complete a work in 12 days and 15 days respectively. In how many days can they complete the work together?
Correct Answer: 6.67 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 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 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: To find out how many days they take to complete the work together, take the reciprocal of their combined work rate: 1 / (3/20) = 20/3 days.
  • Step 10: Convert 20/3 days to a decimal to find the approximate number of days: 20/3 = 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 and simplifying the result.
  • Time Calculation – Calculating the total time taken to complete a task based on combined work rates.
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