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Two worker A and B working together completed a job in 5 days.if a had worked twice as efficency as he actually did the work would have been completed in 3 days.To completed the job alone a would require
a25/2
b25/4
c15/2
d35/3?
a25/2
b25/4
c15/2
d35/3?
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Two worker A and B working together completed a job in 5 days.if a had...
To determine how long worker A would take to complete the job alone, we first need to analyze the information given about the work done by both A and B together.
Joint Work of A and B
- Workers A and B together complete the job in 5 days.
- Let the total work be represented as W.
- Thus, the combined work rate of A and B is:
- Rate (A + B) = W / 5
A's Increased Efficiency
- If A worked with twice his efficiency, the job would be completed in 3 days.
- In this case, the new work rate of A is:
- Rate (2A + B) = W / 3
Setting Up the Equations
- From the first scenario:
- A + B = W / 5 (Equation 1)
- From the second scenario:
- 2A + B = W / 3 (Equation 2)
Solving the Equations
- Subtract Equation 1 from Equation 2:
- (2A + B) - (A + B) = (W / 3) - (W / 5)
- A = (5W - 3W) / 15 = 2W / 15
- Substitute A in Equation 1 to find B:
- (2W / 15) + B = W / 5
- B = (W / 5) - (2W / 15)
- B = (3W - 2W) / 15 = W / 15
Time Taken by A Alone
- Now, to find the time A takes to complete the work alone:
- Time (A alone) = W / A = W / (2W / 15) = 15 / 2 = 7.5 days
Conclusion
- Therefore, worker A would require 7.5 days to complete the job alone.
Joint Work of A and B
- Workers A and B together complete the job in 5 days.
- Let the total work be represented as W.
- Thus, the combined work rate of A and B is:
- Rate (A + B) = W / 5
A's Increased Efficiency
- If A worked with twice his efficiency, the job would be completed in 3 days.
- In this case, the new work rate of A is:
- Rate (2A + B) = W / 3
Setting Up the Equations
- From the first scenario:
- A + B = W / 5 (Equation 1)
- From the second scenario:
- 2A + B = W / 3 (Equation 2)
Solving the Equations
- Subtract Equation 1 from Equation 2:
- (2A + B) - (A + B) = (W / 3) - (W / 5)
- A = (5W - 3W) / 15 = 2W / 15
- Substitute A in Equation 1 to find B:
- (2W / 15) + B = W / 5
- B = (W / 5) - (2W / 15)
- B = (3W - 2W) / 15 = W / 15
Time Taken by A Alone
- Now, to find the time A takes to complete the work alone:
- Time (A alone) = W / A = W / (2W / 15) = 15 / 2 = 7.5 days
Conclusion
- Therefore, worker A would require 7.5 days to complete the job alone.
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Two worker A and B working together completed a job in 5 days.if a had worked twice as efficency as he actually did the work would have been completed in 3 days.To completed the job alone a would require a25/2b25/4c15/2d35/3?
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