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Question 66
C is 20% more efficient than A. A and B together can finish a piece of work in 16 days. B and C together can do it in 15 days. In how many days A alone can finish the same piece of work ?
Solution
Let rate of doing work be 1/A , 1/B and 1/C.
((1/A) + (1/B)) = 1/16 ----------------1
((1/B) + (1/C)) = 1/15 ----------------2
C is 20% more efficient than A.
1/C = 12/10A
Replacing 1/C in 2.
((1/B) + (12/10A)) = 1/15 ------------3
From 1
1/B = (1/16) - (1/A)
Replacing (1/B) in 3
(1/16) - (1/A) + (12/10A) = 1/15
2/10A = (1/15) - (1/16)
2/10A = 1/240
1/A = 1/48
A alone takes 48 days to complete the work.
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