Question

A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.

1. How long will it take them to do the work together?
2. In what time can each finish it working alone?

Answer 1

A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C and A can do a piece of work in = 24 days
(A+B)’s 1-day work =`1/40`

(B+C)’s 1-day work =`1/30`

(C+A)’s 1-day work =`1/24`

(i) [(A+B)+(B+C)+(C+A)]’s 1 day work = `1/40+1/30+1/24`

`=(3+4+5)/120`

`=12/120=1/10`

i.e. (A+B+B+C+C+A)'s 1-day work =`1/10`

i.e. 2 (A+B+C)'s 1-day work =`1/10`

∴ (A+B+C)'s 1-day work =`1/10xx1/2`

`=1/20`

∴ (A+B+C) can do the work in = 20 days

(ii) A's 1-day work =`1/20-1/30`

`=(3-2)/60=1/60`

∴ A can do the work in 60 days

B's 1-day work =`1/20-1/24`

`=(6-5)/120=1/120`

∴ B can do the work in 120 days

 now, C's 1-day work =`1/20-1/40`

`=(2-1)/40=1/40`

C can do the work in 40 days

Hence A can do the work in = 60 days

B can do the work in = 120 days

C can do the work in = 40 days