Question : A and B can do a piece of work in 8 days, B and C can do it in 24 days while C and A can do it in $8\frac{4}{7}$ days. In how many days can C do it alone?
Option 1: 60 days
Option 2: 40 days
Option 3: 30 days
Option 4: 10 days
Correct Answer: 60 days
Solution :
Given: A and B can do a piece of work in 8 days. B and C can do it in 24 days, and A and C can do it in $\frac{60}{7}$ days.
(A+B)'s 1 day's work = $\frac{1}{8}$
(B+C)'s 1 day's work = $\frac{1}{24}$
(A+C)'s 1 day's work = $\frac{7}{60}$
Adding the above three equations we get,
2(A+B+C)'s 1 day's work = $\frac{1}{8}+\frac{1}{24}+\frac{7}{60}=\frac{15+5+14}{120} = \frac{34}{120} = \frac{17}{60}$
⇒ (A+B+C)'s 1 day's work is $\frac{17}{120}$.
C's 1 days's work $=\frac{17}{120} - \frac{1}{8} = \frac{17–15}{120} = \frac{2}{120} = \frac{1}{60}$
So, C can alone complete the work in 60 days.
Hence, the correct answer is 60 days.
Related Questions
Know More about
Staff Selection Commission Multi Tasking ...
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Get Updates Brochure
Your Staff Selection Commission Multi Tasking Staff Exam brochure has been successfully mailed to your registered email id “”.
