Q) A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

a) 4 days                     b) 6 days             c) 8 days                     d) 12 days

Ans:

Method 1:

(A + B)’s 1 day work = 1/8

(B + C)’s 1 day’s work = 1/12

Let’s consider, (A + C)’s 1 day’s work = 1/X

By adding all the above 3 equations, we get:

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

= 1/8 + 1/12 + 1/X = 5/24 + 1/X

∴ 2 x (A + B + C)’s 1 day’s work = 5/24 + 1/X

∴ (A + B + C)’s 1 day’s work = 5/48 + 1/2X

Given that, (A + B + C)’s 1 day’s work = 1/6

∴ 5/48 + 1/2X = 1/6

1/2X = 1/6 – 5/48 = 3/48 = 1/16

X = 16/2 = 8 days

Method 2:

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

∴  1/A = 1/6 – 1/12 = 1/12

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

∴ 1/C = 1/6 – 1/8 = 1/24

∴  (A + C)’s 1 day work = A’s 1 day work + C’s 1 day work

∴ 1/12 + 1/24 = 3/24 = 1/8

Since time taken by A to complete 1/8 work = 1 day

time taken by A to complete full work = 1/(1/8) = 8 days