Number of days required by A and B to finish the work : 12 days
Number of days required by A and B to finish the work : 15 days
Number of days required by A and B to finish the work : 20 days
Work done by A and B in one day: \(\frac{1}{12}\)
Work done by B and C in one day: \(\frac{1}{15}\)
Work done by C and A in one day: \(\frac{1}{20}\)
Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by
(A + B) + (B + C) + (C + A) = 2(A + B + C) = \(\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{12}{60}=\frac{1}{5}\)
∴ Work done by A, B and C = \(\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}\)
A ‘s one day work = (A +B + C ) ‘s one day work – (B + C) ‘s one day work
= \(\frac{1}{10}-\frac{1}{15}=\frac{1}{30}\)
∴ A alone can complete the work in 30 days.
