**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. … ? (ii) In what time can each finish it…**

###### Answers:

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 = 1/10 × ½

= 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