Question

A and b can do a piece of work in 72 days. b and c can do it in 120 days, a and c can do it in 90 day.thrn a alone can do rhe work in

Answer 1

Hey.

Here is the answer.
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Let A can do the complete work alone in a days
so, work done in one day by A = 1/a
similarly let one day work by B = 1/b
similarly let one day work by C =1/c

then according to question ,
as both A and B do the work in 72 days so,
one day work by both a&b =(1/a +1/b )= 1/72

Similarly , by b &c =(1/b +1/c) =1/120

Similarly, by a & c = (1/a +1/ c)= 1/90

we have three equations and three unknowns, so substracting 3rd from 1st , we get ,

1/b -1/c = 1/72 -1/90= (10-8)/720=2/720=1/360
adding this equation to 2nd equation , we get

2×1/b = 1/120+1/360 = (3+1)/360=1/90
so, 2/b = 1/90

so, b= 2×90=180 days

Also, 1/180 -1/c = 1/360
so, 1/c = 1/180-1/360=(2-1)/360= 1/360

so, c = 360 days

Hence , 1/a + 1/180= 1/72
so, 1/a = 1/72 - 1/180= (10-4)/720=6/720=1/120

so, a = 120 days
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Thanks.