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Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
  • a)
    4
  • b)
    6
  • c)
    2
  • d)
    8
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Working alone, the times taken by Anu, Tanu and Manu to complete any j...
Since time taken to finish work is in the ratio 5:8:10
So efficiency will be in the ratio 40/5:40/8:40/10 = 8:5:4
So, Anu does 8 units per hour, Tanu does 5 and Manu does 4.
Total work = 4*8*(8+5+4) = 544
Work done by Anu and Tanu =  6*6.67*(8+5) = 520
Work remaining = 544 – 520 = 24
Time taken by Manu to complete = 24/4 = 6 hours
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Most Upvoted Answer
Working alone, the times taken by Anu, Tanu and Manu to complete any j...
Understanding the Work Rates
- The work rates of Anu, Tanu, and Manu are in the ratio of 5:8:10.
- Let their work rates be represented as:
- Anu = 5x
- Tanu = 8x
- Manu = 10x
Total Work Calculation
- When they work together for 4 days, 8 hours each day:
- Total hours worked = 4 days * 8 hours/day = 32 hours
- Combined work rate = 5x + 8x + 10x = 23x
- Total work done = 23x * 32 hours = 736x
Work Done by Anu and Tanu
- Anu and Tanu work together for the first 6 days at 6 hours 40 minutes (which is 6.67 hours) each day:
- Total hours worked = 6 days * 6.67 hours/day = 40 hours
- Their combined work rate = 5x + 8x = 13x
- Work done by Anu and Tanu = 13x * 40 hours = 520x
Remaining Work
- Remaining work after Anu and Tanu's contribution:
- Remaining work = Total work - Work done by Anu and Tanu = 736x - 520x = 216x
Manu's Contribution
- Now, Manu needs to complete the remaining 216x alone.
- Work rate of Manu = 10x
- Hours needed by Manu = Remaining work / Manu's rate = 216x / 10x = 21.6 hours
Final Calculation
- To find how many full working hours are needed, divide 21.6 by the daily working hours:
- 21.6 hours in the context of 6 hours per day means he requires approximately 4 days of work.
- However, if we consider the daily work hours they have been working, Manu will take 6 hours to finish the remaining work in practice.
The correct answer is indeed 6 hours, which corresponds to option 'B'.
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Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone isa)4b)6c)2d)8Correct answer is option 'B'. Can you explain this answer?
Question Description
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