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Manoj is 2 times efficient than Anurag, together they can complete the work in 22 days. Anurag alone can complete the work in how many days?
- a)44
- b)66
- c)88
- d)60
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Manoj is 2 times efficient than Anurag, together they can complete the...
Let Anurag alone can do a piece of work in ‘x’ days.
⇒ Work done by Anurag in one day = 1/x
⇒ Work done by Manoj in one day = 2/x
Work done by Manoj and Anurag together in one day = 2/x + 1/x = 3/x
⇒ Time taken by Manoj and Anurag together to complete the work = 1/(3/x) = x/3
⇒ 22 = x/3
⇒ x = 66 days
∴ Time taken by Anurag alone to complete the work = 66 days
⇒ Work done by Anurag in one day = 1/x
⇒ Work done by Manoj in one day = 2/x
Work done by Manoj and Anurag together in one day = 2/x + 1/x = 3/x
⇒ Time taken by Manoj and Anurag together to complete the work = 1/(3/x) = x/3
⇒ 22 = x/3
⇒ x = 66 days
∴ Time taken by Anurag alone to complete the work = 66 days
Most Upvoted Answer
Manoj is 2 times efficient than Anurag, together they can complete the...
Understanding the Problem
To find out how many days Anurag alone can complete the work, we first need to analyze the efficiency of Manoj and Anurag.
Efficiency Relationship
- Manoj is 2 times as efficient as Anurag.
- If we denote Anurag's efficiency as "A", then Manoj's efficiency would be "2A".
Work Done Together
- When they work together, their combined efficiency is:
- Combined Efficiency = A + 2A = 3A
- They can complete the work in 22 days, which means their total work can be represented as:
- Total Work = Combined Efficiency × Time
- Total Work = 3A × 22 = 66A
Finding Anurag's Work Rate
- Now, we need to determine how long Anurag takes to complete the work alone.
- Anurag alone can complete the work at a rate of "A" per day.
Calculating Anurag's Time
- The time taken by Anurag to complete the total work is given by:
- Time = Total Work ÷ Anurag's Efficiency
- Time = 66A ÷ A = 66 days
Conclusion
Thus, Anurag alone can complete the work in 66 days. Therefore, the correct answer is option 'B'.
To find out how many days Anurag alone can complete the work, we first need to analyze the efficiency of Manoj and Anurag.
Efficiency Relationship
- Manoj is 2 times as efficient as Anurag.
- If we denote Anurag's efficiency as "A", then Manoj's efficiency would be "2A".
Work Done Together
- When they work together, their combined efficiency is:
- Combined Efficiency = A + 2A = 3A
- They can complete the work in 22 days, which means their total work can be represented as:
- Total Work = Combined Efficiency × Time
- Total Work = 3A × 22 = 66A
Finding Anurag's Work Rate
- Now, we need to determine how long Anurag takes to complete the work alone.
- Anurag alone can complete the work at a rate of "A" per day.
Calculating Anurag's Time
- The time taken by Anurag to complete the total work is given by:
- Time = Total Work ÷ Anurag's Efficiency
- Time = 66A ÷ A = 66 days
Conclusion
Thus, Anurag alone can complete the work in 66 days. Therefore, the correct answer is option 'B'.
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Manoj is 2 times efficient than Anurag, together they can complete the work in 22 days. Anurag alone can complete the work in how many days?a)44b)66c)88d)60Correct answer is option 'B'. Can you explain this answer?
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