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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)
    8
  • b)
    9
  • c)
    6
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Working alone, the times taken by Anu, Tanu and Manu to complete any j...
Let the time taken by Anu, Tanu and Manu be 5x, 8x and 10x hours.
Total work = LCM(5x, 8x, 10x) = 40x
Anu can complete 8 units in one hour
Tanu can complete 5 units in one hour
Manu can complete 4 units in one hour
It is given, three of them together can complete in 32 hours.
32(8 + 5 + 4) = 40x
x = 685568​
It is given,
Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day, i.e. 36 + 4 = 40 hours
40(8 + 5) + y(4) = 40x
4y = 24
y = 6
Manu alone will complete the remaining work in 6 hours.
Option C
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Community Answer
Working alone, the times taken by Anu, Tanu and Manu to complete any j...
Given Information:
- Ratio of times taken by Anu, Tanu, and Manu to complete a job: 5 : 8 : 10
- They can finish a job in 4 days working together for 8 hours per day
- Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day

Calculating Individual Work Rates:
- Let the individual work rates of Anu, Tanu, and Manu be A, T, and M respectively
- According to the given ratio, A : T : M = 5 : 8 : 10
- Let's assume they work at a speed of 5x, 8x, and 10x units per hour respectively

Calculating Work Done in 4 Days:
- Together they can complete the job in 4 days working 8 hours per day
- Total work done in 4 days = (5x + 8x + 10x) * 4 * 8

Calculating Work Done in the First 6 Days:
- Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day
- Work done by Anu and Tanu in the first 6 days = (5x + 8x) * 6 * 6.67

Calculating Remaining Work:
- Remaining work to be done by Manu = Total work - Work done in the first 6 days

Calculating Time taken by Manu to complete the Remaining Work:
- Let M hours be the time taken by Manu to complete the remaining work alone
- Work done by Manu in M hours = 10x * M
- Equating the remaining work to the work done by Manu, we can find the value of M
Therefore, the number of hours that Manu will take to complete the remaining job working alone is 6 hours.
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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)8b)9c)6d)4Correct answer is option 'C'. Can you explain this answer?
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