A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?
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A and B can do a piece of work in = 12 days
Work done by A and B in 1 day = 1/12
B and C can do a piece of work in = 15 days
Work done by B and C in 1 day = 1/15
A and C can do a piece of work in = 20 days
Work done by A and C in 1 day = 1/20
By adding A, B and C we get,
2(A+B+C)’s one day work = 1/12 + 1/15 + 1/20 = (5+4+3)/60
(by taking LCM for 12, 15 and 20 which is 60) = 12/60 = 1/5 A+B+C one day work = 1/(5×2) = 1/10
We know that,
A’s 1 day work = (A+B+C)’s 1 day work – (B+C)’s 1 day work
= 1/10 – 1/15
= (3-2)/30
(by taking LCM for 10 and 15 which is 30)
= 1/30
∴ A alone can finish the work in = 1/(1/30) =30days.
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