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A can complete a work in 10 days, while B can complete the same work in 15 days.

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Question: A can complete a work in 10 days, while B can complete the same work in 15 days. If both work together, how many days will they take to complete the work?

Options:

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

Correct Answer: 6

Solution: 

A\'s work rate = 1/10, B\'s work rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. They will complete the work in 6 days.

A can complete a work in 10 days, while B can complete the same work in 15 days.

Practice Questions

Q1
A can complete a work in 10 days, while B can complete the same work in 15 days. If both work together, how many days will they take to complete the work?
  1. 5
  2. 6
  3. 7
  4. 8

Questions & Step-by-Step Solutions

A can complete a work in 10 days, while B can complete the same work in 15 days. If both work together, how many days will they take to complete the work?
  • Step 1: Determine A's work rate. A can complete the work in 10 days, so A's work rate is 1/10 of the work per day.
  • Step 2: Determine B's work rate. 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 done by calculating 1/10 + 1/15.
  • Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
  • Step 5: Convert 1/10 to a fraction with a denominator of 30. This gives us 3/30.
  • Step 6: Convert 1/15 to a fraction with a denominator of 30. This gives us 2/30.
  • Step 7: Now add the two fractions: 3/30 + 2/30 = 5/30.
  • Step 8: Simplify 5/30 to 1/6. This means A and B together can complete 1/6 of the work in one day.
  • Step 9: To find out how many days they will take to complete the entire work, take the reciprocal of their combined work rate: 1 / (1/6) = 6 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 combined work rates.
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