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A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all wo

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Question: A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all work together, how long will it take to complete the work?

Options:

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

Correct Answer: 6 days

Solution: 

Combined rate = (1/16 + 1/24 + 1/32) = 1/8. Therefore, they will complete the work in 8 days.

A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all wo

Practice Questions

Q1
A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all work together, how long will it take to complete the work?
  1. 6 days
  2. 8 days
  3. 10 days
  4. 12 days

Questions & Step-by-Step Solutions

A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all work together, how long will it take to complete the work?
  • Step 1: Determine the work rate of each person. A can complete the work in 16 days, so A's rate is 1/16 of the work per day.
  • Step 2: B can complete the work in 24 days, so B's rate is 1/24 of the work per day.
  • Step 3: C can complete the work in 32 days, so C's rate is 1/32 of the work per day.
  • Step 4: Add the rates of A, B, and C together to find their combined work rate: 1/16 + 1/24 + 1/32.
  • Step 5: To add these fractions, find a common denominator. The least common multiple of 16, 24, and 32 is 48.
  • Step 6: Convert each fraction to have the common denominator of 48: 1/16 = 3/48, 1/24 = 2/48, and 1/32 = 1.5/48.
  • Step 7: Now add the fractions: 3/48 + 2/48 + 1.5/48 = 6.5/48.
  • Step 8: Simplify the combined rate: 6.5/48 = 1/8.
  • Step 9: The combined rate of 1/8 means they can complete 1/8 of the work in one day.
  • Step 10: To find out how many days it takes to complete the entire work, take the reciprocal of the combined rate: 1 / (1/8) = 8 days.
  • Work Rate – Understanding how to calculate the combined work rate of multiple workers based on their individual completion times.
  • Fraction Addition – Ability to add fractions with different denominators to find a common work rate.
  • Reciprocal Relationships – Recognizing that the time taken to complete work is the reciprocal of the combined work rate.
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