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A and B can complete a work in 12 days. B and C can complete the same work in 15

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Question: A and B can complete a work in 12 days. B and C can complete the same work in 15 days. If A, B, and C work together, how many days will they take to complete the work?

Options:

  1. 5 days
  2. 6 days
  3. 7 days
  4. 8 days

Correct Answer: 6 days

Solution: 

Work done by A and B in one day = 1/12. Work done by B and C in one day = 1/15. Let work done by B in one day = x. Then, A\'s work = 1/12 - x and C\'s work = 1/15 - x. Solving gives A + B + C = 1/8. Therefore, they will complete the work in 8 days.

A and B can complete a work in 12 days. B and C can complete the same work in 15

Practice Questions

Q1
A and B can complete a work in 12 days. B and C can complete the same work in 15 days. If A, B, and C work together, how many days will they take to complete the work?
  1. 5 days
  2. 6 days
  3. 7 days
  4. 8 days

Questions & Step-by-Step Solutions

A and B can complete a work in 12 days. B and C can complete the same work in 15 days. If A, B, and C work together, how many days will they take to complete the work?
  • Step 1: Understand that A and B can complete the work in 12 days. This means together they do 1/12 of the work in one day.
  • Step 2: Understand that B and C can complete the work in 15 days. This means together they do 1/15 of the work in one day.
  • Step 3: Let the amount of work done by B in one day be represented as 'x'.
  • Step 4: From Step 1, we know A and B together do 1/12 of the work in one day. Therefore, A's work can be expressed as (1/12 - x).
  • Step 5: From Step 2, we know B and C together do 1/15 of the work in one day. Therefore, C's work can be expressed as (1/15 - x).
  • Step 6: Now we have expressions for A's work, B's work, and C's work: A = (1/12 - x), B = x, C = (1/15 - x).
  • Step 7: Add the work done by A, B, and C together: (1/12 - x) + x + (1/15 - x) = 1/12 + 1/15 - x.
  • Step 8: Combine the fractions 1/12 and 1/15. The least common multiple of 12 and 15 is 60. So, 1/12 = 5/60 and 1/15 = 4/60. Therefore, 1/12 + 1/15 = 5/60 + 4/60 = 9/60.
  • Step 9: Now we have: 9/60 - x = A + B + C. To find A + B + C, we need to solve for x.
  • Step 10: Since we want to find A + B + C, we can set it equal to 9/60. Therefore, A + B + C = 9/60 = 3/20.
  • Step 11: To find out how many days A, B, and C will take to complete the work together, we take the reciprocal of 3/20, which is 20/3 days.
  • Step 12: Convert 20/3 days into a mixed number: 20/3 = 6 days and 2/3 of a day.
  • Work Rate – Understanding how to calculate the work done by individuals and groups based on their rates.
  • Algebraic Manipulation – Using algebra to express individual work rates in terms of a common variable.
  • Combined Work – Calculating the total work rate when multiple individuals work together.
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