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A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work to

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Question: A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work together for 2 days, how much work is left?

Options:

  1. 1/4
  2. 1/3
  3. 1/2
  4. 1/6

Correct Answer: 1/3

Solution: 

A\'s rate = 1/8, B\'s rate = 1/12, C\'s rate = 1/24. Combined rate = 1/8 + 1/12 + 1/24 = 1/4. Work done in 2 days = 2/4 = 1/2. Remaining work = 1 - 1/2 = 1/2.

A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work to

Practice Questions

Q1
A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work together for 2 days, how much work is left?
  1. 1/4
  2. 1/3
  3. 1/2
  4. 1/6

Questions & Step-by-Step Solutions

A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work together for 2 days, how much work is left?
  • Step 1: Determine how much work A, B, and C can do in one day.
  • Step 2: Calculate A's work rate: A can complete the work in 8 days, so A's rate is 1/8 of the work per day.
  • Step 3: Calculate B's work rate: B can complete the work in 12 days, so B's rate is 1/12 of the work per day.
  • Step 4: Calculate C's work rate: C can complete the work in 24 days, so C's rate is 1/24 of the work per day.
  • Step 5: Add the work rates of A, B, and C to find their combined work rate: 1/8 + 1/12 + 1/24.
  • Step 6: Find a common denominator to add the fractions: The common denominator for 8, 12, and 24 is 24.
  • Step 7: Convert each rate to have the common denominator: A's rate = 3/24, B's rate = 2/24, C's rate = 1/24.
  • Step 8: Add the converted rates: 3/24 + 2/24 + 1/24 = 6/24.
  • Step 9: Simplify the combined rate: 6/24 simplifies to 1/4.
  • Step 10: Calculate how much work they do together in 2 days: Work done in 2 days = 2 * (1/4) = 2/4 = 1/2.
  • Step 11: Determine the remaining work: Total work is 1, so remaining work = 1 - 1/2 = 1/2.
  • Work Rate – Understanding how to calculate individual and combined work rates of multiple workers.
  • Fraction Addition – Adding fractions with different denominators to find a combined work rate.
  • Work Completion – Determining the amount of work completed and the remaining work after a certain period.
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