Question

A and B together can do a piece of work in 12
days, which B and C together can do in 16 days.
After A has been working at it for 5 days and B
for 7 days, C finishes it in 13 days. In how many
days C alone will do the work?
(a) 16 (b) 24
(c) 37 (d) 48

Answer 1

Let’s solve this question arithmetically :

As A and B can finish the work in 12 days time, hence

(A + B)’s one day’s work = 1/12;

similarly

(B + C)’s one day’s work = 1/16

Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1

A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1

Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1

i.e. 5/12 + 2/16 + C’s 11 days’ work = 1

or C’s 11 days’ work = 1 - (5/12 + 2/16)

or C’s 11 days’ work = 1 - 13/24

or C’s 11 days’ work = 11/24

or C’s 1 day’s work = 11/24 x 1/11 = 1/24

Therefore, C alone can finish the complete work in 24 days.