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A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually?
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A is two times more efficient than B ,if they complete the work in 30 ...
Understanding Efficiency
When we say A is two times more efficient than B, it means if B completes a task in a certain number of days, A can complete the same task in half that time.
Work Completed in 30 Days
Together, A and B can complete the work in 30 days. This implies that their combined work rate can be calculated as follows:
- Let B's efficiency be \( x \) (work done per day).
- Then A's efficiency will be \( 2x \).
- Therefore, together they work at a rate of \( x + 2x = 3x \).
Since they complete the work in 30 days, we can establish the equation:
- Total work = \( 3x \times 30 = 90x \).
Individual Work Rates
Now, we can find out how long each person takes to complete the work individually.
- For A:
- A's rate = \( 2x \).
- Days required by A = \( \frac{Total \ Work}{A's \ Efficiency} = \frac{90x}{2x} = 45 \) days.
- For B:
- B's rate = \( x \).
- Days required by B = \( \frac{Total \ Work}{B's \ Efficiency} = \frac{90x}{x} = 90 \) days.
Final Results
- A takes 45 days to complete the work individually.
- B takes 90 days to complete the work individually.
This shows the difference in their efficiencies and how it impacts their work completion times.
When we say A is two times more efficient than B, it means if B completes a task in a certain number of days, A can complete the same task in half that time.
Work Completed in 30 Days
Together, A and B can complete the work in 30 days. This implies that their combined work rate can be calculated as follows:
- Let B's efficiency be \( x \) (work done per day).
- Then A's efficiency will be \( 2x \).
- Therefore, together they work at a rate of \( x + 2x = 3x \).
Since they complete the work in 30 days, we can establish the equation:
- Total work = \( 3x \times 30 = 90x \).
Individual Work Rates
Now, we can find out how long each person takes to complete the work individually.
- For A:
- A's rate = \( 2x \).
- Days required by A = \( \frac{Total \ Work}{A's \ Efficiency} = \frac{90x}{2x} = 45 \) days.
- For B:
- B's rate = \( x \).
- Days required by B = \( \frac{Total \ Work}{B's \ Efficiency} = \frac{90x}{x} = 90 \) days.
Final Results
- A takes 45 days to complete the work individually.
- B takes 90 days to complete the work individually.
This shows the difference in their efficiencies and how it impacts their work completion times.
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A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually?
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A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually?.
A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A is two times more efficient than B ,if they complete the work in 30 days, then find the days required by each to complete the work individually?.
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