Question

A and b together can do a piece of work in 16 days and b and c can do the same work in 24 days. from starting a and b worked for 4 days and 7 days respectively and remaining work is completed by c in 23 days, then find in how many days will c complete the work alone? (a) 32 days (b) 16 days (c) 8 days (d) 24 days (e) 36 days

Answer 1

I solved it like this 

Let's say rate of A is R1 work/day, 
rate of B is R2 work/day, and 
rate of C is R3 work/day 

Based on the information we have we know that 

R1 + R2 = 1/12 ---------------------- 1 
R2 + R3 = 1/16----------------------- 2 
5R1 + 7R2 + 13R3 = 1 -------------- 3 

Let's solve equation 3 for R2 

5(1/12 - R2) + 7R2 + 13(1/16 - R2) = 1 

5/12 - 5R2 + 7R2 + 13/16 - 13R2 = 1 

5/12 + 13/16 -11R2 = 1 

Therefore, 11R2 = 5/12 + 13/16 
R2 = 1/11(5/12 + 13/16) 
R2 = 0.11 

We need to find R3 though, we know from 2 that 
R3 = 1/16 - R2 
R3 = 1/16 - 0.11 
R3 = -0.0475 

But rate cannot be negative hence 
R3 = 0.0475 w/day 
Hence in order to finish 1 work R3 will take 1/0.0475 = 21 days