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

The Correct Option is C

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