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A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!?
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A and B together can do a piece of work in 15 days while be alone can ...
Understanding the Problem
To find out how many days A alone can finish the work, we need to analyze the rates of work done by A and B.
Work Done by A and B Together
- A and B together can complete the work in 15 days.
- Therefore, their combined work rate is 1/15 of the work per day.
Work Done by B Alone
- B alone can finish the work in 20 days.
- Hence, B's work rate is 1/20 of the work per day.
Finding A's Work Rate
- Let A's work rate be 1/x of the work per day.
- The combined work rate of A and B can be expressed as:
(1/x) + (1/20) = 1/15
- To solve for A's work rate, we first find a common denominator.
Solving the Equation
- Multiply through by 60 (the least common multiple of 15 and 20) to eliminate the denominators:
60 * (1/x) + 60 * (1/20) = 60 * (1/15)
- This simplifies to:
60/x + 3 = 4
- Rearranging gives:
60/x = 1
- Therefore, x = 60.
Conclusion
- A can complete the work alone in 60 days.
- Hence, A alone can finish the work in 60 days.
To find out how many days A alone can finish the work, we need to analyze the rates of work done by A and B.
Work Done by A and B Together
- A and B together can complete the work in 15 days.
- Therefore, their combined work rate is 1/15 of the work per day.
Work Done by B Alone
- B alone can finish the work in 20 days.
- Hence, B's work rate is 1/20 of the work per day.
Finding A's Work Rate
- Let A's work rate be 1/x of the work per day.
- The combined work rate of A and B can be expressed as:
(1/x) + (1/20) = 1/15
- To solve for A's work rate, we first find a common denominator.
Solving the Equation
- Multiply through by 60 (the least common multiple of 15 and 20) to eliminate the denominators:
60 * (1/x) + 60 * (1/20) = 60 * (1/15)
- This simplifies to:
60/x + 3 = 4
- Rearranging gives:
60/x = 1
- Therefore, x = 60.
Conclusion
- A can complete the work alone in 60 days.
- Hence, A alone can finish the work in 60 days.
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A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!?
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A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!?.
A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B together can do a piece of work in 15 days while be alone can finish it in 20 days in how many days can A alone finish the work!?.
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