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Question 828251: Dinu and Hemu can plough a field in 15 days. If Dinu alone can plough 1/8 of the field in 5 days, how many days will hemu take to do the same work alone?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=time it takes Hemu to do the same work alone
So Hemu ploughs at the rate of 1/x of the field per day
Together Dinu and Hemu ploughs at the rate of 1/15 of the field per day
But we are told that Dinu alone can plough 1/8 of the field in 5 days. This means that he can plough 8/8 of the field (the whole field) in 8*5=40 days. So Dinu works at the rate of 1/40 of the field per day(In 5 days, Dinu ploughs 5/40= 1/8 of the field, as stated)
So, our equation to solve is:
1/x + 1/40 = 1/15 multiply each term by 120x
120 + 3x=8x
5x=120
x=24 days----time it takes Hemu working alone
CK
In 15 days, Hemu ploughs 15/24 of the field
In 15 days Dinu ploughs 15/40 of the field
Now 15/24 +15/40 should equal 1 (field, that is)
75/120 + 45/120 = 1
120/120=1
CK
Hope this helps---ptaylor
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