Question

a &b can do a piece of work in 12 days b & c in 16 days respectively. after a has been working for 5 days and b for 7 days c takes up and finishes it alone in 13 days. in how many days they can do it separately?

Answer 1

A and B together can do a piece of work in 12 days which B and C together will do in 16 days. After A has been working on it for 5 days, and B for 7 days, C finishes it in 13 days. In how many days A,B and C alone will do the work ?
(A + B) one day work = 100/12 = 8.33% per day.
(B + C) one day work = 100/16 = 6.25% per day.
Now, according to question,
(A + B)'s 5 days work + (B + C)'s 2 days work + C's 11 days work = 1
[5 days work of B has been included with A and 2 das work of C has been included with B.]
(8.33 * 5 )+ (2 *6.25) + C's 11 days work = 100%
C's 13 days work = 100 - 41.66 - 12.5 = 45.84%
So, one day work of C = 45.84/11 = 4.16%
C can done work = 100/4.16 = 24 days
B + C = 6.25
B = 6.25 – 4.16= 2.09% per day work.
B can finish 100% work = 100/2.09 = 48 days.
A + B = 8.33
A = 8.33 – B
A = 8.33 – 2.09 = 6.24.
A can finish 100% work in = 100/6.24 = 16 days.