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need explanation for this solution


sonur

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2.If 9 men working 15/2 hrs a day can finish a piece of work in 20 days, then how many days will be taken by 12 men, working 6 hrs a day to finish the work, it being given that 2 men of latter type work as much as 3 men of the former type?

1 19/2 b 11 c 25/2 d 13

 

Solution by arjmen:

Work = 9*r*(15/2)*20 = 12*r'*6*d, where r and r' are the respective rates of work

r' = (3/2)r

=> 9*15*10 = 6*3*6*d

=> d = 9*15*10/(6*3*6) = 25/2 days

 

could you please explain the how did you get r'=(3/2)r ????kindly explain ???the solution in detail...i appreciate your help thx

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Say you have 2 people in both types of work:

 

let r be the first-type workers' rate and r' be the second-type workers' rate.

Work done by the people of second type= 2 * r' * time.

But it is GIVEN that these two people of the second type can work as much as the THREE people of the first type in the same amount of time.

 

Therefore,

Work done by the people of secondtype

= 2 * r' * time = 3*r*time

=>r'=3/2 * r

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