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A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
- a)18 days
- b)27 days
- c)26.67 days
- d)16 days
- e)12 days
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A can complete a project in 20 days and B can complete the same projec...
Understanding the Problem
To solve this problem, we need to understand the individual work rates of A and B, and how their combined work rate changes when A quits 10 days before the project is completed.
Solving the Problem
1. Work Rates of A and B:
- A completes the project in 20 days, so A's work rate is 1/20 of the project per day.
- B completes the project in 30 days, so B's work rate is 1/30 of the project per day.
2. Combined Work Rate:
- When A and B work together, their combined work rate is the sum of their individual work rates.
- Therefore, A and B's combined work rate is 1/20 + 1/30 = 1/12 of the project per day.
3. Work Done by A before Quitting:
- Since A quits 10 days before the project is completed, A works for 10 days.
- In 10 days, A completes 10 * (1/20) = 1/2 of the project.
4. Remaining Work:
- After A quits, B is left to complete the remaining 1/2 of the project.
- With a combined work rate of 1/12 per day, B will take 1/2 / (1/12) = 6 days to complete the remaining work.
5. Total Time to Complete the Project:
- A worked for 10 days and B worked for 6 days after A quit, so the total time taken to complete the project is 10 + 6 = 16 days.
Therefore, the project will be completed in 16 days, which aligns with option 'A' as the correct answer.
To solve this problem, we need to understand the individual work rates of A and B, and how their combined work rate changes when A quits 10 days before the project is completed.
Solving the Problem
1. Work Rates of A and B:
- A completes the project in 20 days, so A's work rate is 1/20 of the project per day.
- B completes the project in 30 days, so B's work rate is 1/30 of the project per day.
2. Combined Work Rate:
- When A and B work together, their combined work rate is the sum of their individual work rates.
- Therefore, A and B's combined work rate is 1/20 + 1/30 = 1/12 of the project per day.
3. Work Done by A before Quitting:
- Since A quits 10 days before the project is completed, A works for 10 days.
- In 10 days, A completes 10 * (1/20) = 1/2 of the project.
4. Remaining Work:
- After A quits, B is left to complete the remaining 1/2 of the project.
- With a combined work rate of 1/12 per day, B will take 1/2 / (1/12) = 6 days to complete the remaining work.
5. Total Time to Complete the Project:
- A worked for 10 days and B worked for 6 days after A quit, so the total time taken to complete the project is 10 + 6 = 16 days.
Therefore, the project will be completed in 16 days, which aligns with option 'A' as the correct answer.
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Community Answer
A can complete a project in 20 days and B can complete the same projec...
A can complete a project in 20 days. So, A will complete 1/20th of the project in a day.
B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.
B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.
Let the total number of days taken to complete the project be 'x' days.
The value of x is the answer to the question.
The value of x is the answer to the question.
B worked all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.
In a day, A completes 1/20th of the project.
Therefore, A would have completed
of the project in (x - 10) days.
Therefore, A would have completed
of the project in (x - 10) days.In a day, B completes 1/30th of the project.
Therefore, B would have completed x/30th of the project in x days.
3x - 30 + 2x = 60
5x = 90 or x = 18
Therefore, B would have completed x/30th of the project in x days.
3x - 30 + 2x = 60
5x = 90 or x = 18
Choice A is the correct answer.
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A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?a)18 daysb)27 daysc)26.67 daysd)16 dayse)12 daysCorrect answer is option 'A'. Can you explain this answer?
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