Question

A and b take 12 days to finish a piece of work. If b and c work together they take 15 days. While a and c together take 20 days. Find the time taken by each to work alone.

Answer 1

Solutions :-

Given :
A and B take 12 days to finish a piece of work.
(A + B)'s one day work = 1/12

B and C work together they take 15 days.
(B + C)'s one day work = 1/15

A and C together take 20 days.
(A + C)'s one day work = 1/20

{(A + B) + (B + C) + (A + C)}'s one day work = 1/12 + 1/15 + 1/20
=> 2(A + B + C)'s one day work = (5 + 4 + 3)/60
=> (A + B + C)'s one day work = (12)/(60 × 2) = 1/10


A's one day work = (A + B + C)'s one day work - (B + C)'s one day work
= 1/10 - 1/15
= (3 - 2)/30
= 1/30

B's one day work = (A + B + C)'s one day work - (A + C)'s one day work
= 1/10 - 1/20
= (2 - 1)/20
= 1/20

C's one day work = (A + B + C)'s one day work - (A + B)'s one day work
= 1/10 - 1/12
= (6 - 5)/60
= 1/60



Hence,
A alone can do it in 30 days
B alone can do it in 20 days
C alone can do it in 60 days