Question

A and B can do a piece of work in 12 days, while B and C can do it in 15 days where as A and C can do it in 20 days. How long would each take to do the same work?

Answer 1

(A + B) complete the work in 12 days.

∴ (A + B)’s 1 day work = `1/12`  ...(1)

(B + C) complete the work in 15 days

∴ (B + C)’s 1 day work = `1/15`  ...(2)

(A + C) complete the work in 20 days

∴ (A + C)’s 1 day work = `1/20`  ...(3)

Now (1) + (2) + (3) =

[(A + B) + (B + C) + (A + C)]’s 1 day work = `1/12 + 1/15 + 1/20`

(2A + 2B + 2C)’s 1 day work = `5/60 + 4/60 + 3/60`

2(A + B + C)’s 1 day work = `(5 + 4 + 3)/60`

5	12, 15, 20
4	12, 3, 4
3	3, 3, 1
	1, 1, 1

L.C.M = 5 × 4 × 3 = 60

(A + B + C)’s 1 day work = `12/(60 xx 2)`

(A + B + C)’s 1 day work = `1/10`

Now A’s 1 day’s work = (A + B + C)’s 1 day work – (B + C)’s 1 day work

= `1/10 - 1/15`

= `3/30 - 2/30`

= `1/30`

∴ A takes 30 days to complete the work.

B’s 1 day work – (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s work

= `1/10 - 1/20`

= `6/60 - 3/60`

= `(6 - 3)/60`

= `3/60`

= `1/20`

B takes 20 days to complete the work.

C’s 1 day work (A + B + C)’s 1 day work – (A + B)’s 1 day work

= `1/10 - 1/12`

= `6/60 - 5/60`

= `(6 - 5)/60`

= `1/60`

∴ C takes 60 days to complete the work.