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A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together?
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A and B can do a piece of work in 10 days, B and C in 12 days and A an...
Understanding the Problem
To find out how long A, B, and C can complete the work together, we need to analyze the information given about their combined work rates.
Work Rates of Each Pair
- A and B complete the work in 10 days:
- Work rate = 1/10 work/day
- B and C complete the work in 12 days:
- Work rate = 1/12 work/day
- A and C complete the work in 15 days:
- Work rate = 1/15 work/day
Finding Individual Work Rates
Let the work rates of A, B, and C be represented as A, B, and C respectively. We can set up the following equations based on the pair's work rates:
- A + B = 1/10
- B + C = 1/12
- A + C = 1/15
Now, we can add all three equations:
- (A + B) + (B + C) + (A + C) = 1/10 + 1/12 + 1/15
This simplifies to:
- 2A + 2B + 2C = 1/10 + 1/12 + 1/15
Finding the Common Denominator
The least common multiple of 10, 12, and 15 is 60. Thus, converting each fraction, we have:
- 1/10 = 6/60
- 1/12 = 5/60
- 1/15 = 4/60
So,
- 1/10 + 1/12 + 1/15 = (6 + 5 + 4) / 60 = 15/60 = 1/4
Now we have:
- 2A + 2B + 2C = 1/4
This implies:
- A + B + C = 1/8
Final Calculation
Thus, A, B, and C together can complete the work in:
- Time = 1 / (A + B + C) = 1 / (1/8) = 8 days.
Conclusion
A, B, and C can finish the work together in 8 days.
To find out how long A, B, and C can complete the work together, we need to analyze the information given about their combined work rates.
Work Rates of Each Pair
- A and B complete the work in 10 days:
- Work rate = 1/10 work/day
- B and C complete the work in 12 days:
- Work rate = 1/12 work/day
- A and C complete the work in 15 days:
- Work rate = 1/15 work/day
Finding Individual Work Rates
Let the work rates of A, B, and C be represented as A, B, and C respectively. We can set up the following equations based on the pair's work rates:
- A + B = 1/10
- B + C = 1/12
- A + C = 1/15
Now, we can add all three equations:
- (A + B) + (B + C) + (A + C) = 1/10 + 1/12 + 1/15
This simplifies to:
- 2A + 2B + 2C = 1/10 + 1/12 + 1/15
Finding the Common Denominator
The least common multiple of 10, 12, and 15 is 60. Thus, converting each fraction, we have:
- 1/10 = 6/60
- 1/12 = 5/60
- 1/15 = 4/60
So,
- 1/10 + 1/12 + 1/15 = (6 + 5 + 4) / 60 = 15/60 = 1/4
Now we have:
- 2A + 2B + 2C = 1/4
This implies:
- A + B + C = 1/8
Final Calculation
Thus, A, B, and C together can complete the work in:
- Time = 1 / (A + B + C) = 1 / (1/8) = 8 days.
Conclusion
A, B, and C can finish the work together in 8 days.
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A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together?
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A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together?.
A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can do a piece of work in 10 days, B and C in 12 days and A and C in 15 days. In what time can they do it all working together?.
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