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
Started 3 months ago by Shashank in
Explanatory Answer
Time taken by Anu, Tanu and Manu to complete a job is in the ratio 5 : 8 : 10
This means that their efficiencies are in the ratio 15 : 18 : 110
Or, their efficiencies are in the ratios 8 : 5 : 4
This means, for instance, if Anu can wash 8 plates in an hour, Tanu and Manu can wash 5 & 4
plates respectively in one hour.
So, let us remodel the entire question over this imaginary scenario of washing plates…
All three of them finish the job in 4 days working 8 hours per day.
Anu, Tanu and Manu can wash 8, 5 and 4 plates respectively in an hour.
So the total number of plates = (8+5+4)×4×8=17×4×8
Anu and Tanu work together for 6 days, working 6 hours 40 minutes per day.
The total number of plates washed by them = (8+5)×6×623=13×40
So the remaining plates to be washed =17×4×8−13×40
=4(17×8−130)
=4(80+56−130)
=4×6
So, the question is, in how many hours can Manu wash 4×6 plates?
We know that Manu can wash 4 plates in one hour.
Therefore, he requires 6 hours to wash 4×6 plates.
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