Question

A and b together can do a piece of work 12 days.which b and c together can do in 16 days.after a has been working 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 give correct answer with working

Answer 1

Assuming everybody works at constant rate and independent from each other. 

When A works for 5 days and B works for 7 days, we can conclude that A and B work together for 5 days and B works alone for 2 days. And 

Work Rate(A+B) = 1/12 (work/day) 

Thus, Work is done by A and B for 5 days together = 5 days x 1/12 (work/day) = 5/12 work 

When B works for 7-5 = 2 days and C works for 13 day, we can conclude that B and C work together for 2 days and C work alone for 13 - 2 = 11 days. 

Work Rate(B+C) = 1/16 (work/day) 

Thus, Work is done by B and C for 2 days = 2 days x 1/16 (work/day) = 1/8 work 

The remaining job = 1 - 5/12 - 1/8 = (24 - 10 - 3)/24 = 11/24 work 

C can finish this part of work within 11 days. Therefore, the work rate for C = 11/24 (work) x 1/11(1/day) = 1/24 (work/day) 

Or C can finish one work in = 24 days