Question 4

L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together in 90 days. In what time can L alone complete the work?

Solution

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Let L does a units of work/day 
M does b units of work/ day 
N does c units of work/ day 
Now as per given conditions :
Let work be W
So we get
W = 72(a+b) =120(b+c) =90(a+c)
we get
6a+6b = 10b +10c
we get 6a-4b-10c=0   (1)
also
4a+4b =5a+5c
we get a-4b+5c =0   (2)
From (1) and (2)
we get a=3 , b=2 and c=1
Now therefore W = 360
Now time taken by L alone to complete the work = 360/3 = 120 days

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