Question

A and B can finish a job in 10 days while B and C can do it in 18 days. A started the job, worked for 5 days, then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could Catone have finished the whole job?

• A. 30
• B. 15
• C. 45
• D. 24

Answer 1

Answer: (C)

45

Answer 2

Let total work to be done {L.C.M. (10,18)} = 90 units
Let efficiency of A, B and C be $x,y,z$ respectively.
A and B can finish a job in 10 days $=x+y=\frac{90}{10}=9$------(i)
Similarly,$y+z=5$-----(ii)
Adding equations (i) and (ii), $x+2y+z=14$-----(iii)
According to ques, A worked for 5 days, B for 10 days and C for 15 days
$5x+10y+15z=90$
$x+2y+3z=18$-----(iv)
Subtracting equation (iii) from (iv), we get :$2z=4$
$z=2$
Therefore, Time taken by C alone to finish the work=$\frac{90}{2}=45$
The correct answer is (C) :45