Question : Three people A, B, and C worked together and finished a work in 9 days. If A alone can finish the same work in 18 days, and B alone in 30 days, then the number of days C alone will take is:
Option 1: 36 days
Option 2: 45 days
Option 3: 40 days
Option 4: 54 days
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 45 days
Solution :
Let $x$ be the total work.
A alone can finish the same work in 18 days.
So 1 day's work of A = $\frac{1}{18}$ of the work
B alone can finish the same work in 30 days.
So 1 day's work of B = $\frac{1}{30}$ of the work
Let C take $y$ days to complete the work alone.
When A, B, and C work together, their combined work rate is $\frac{1}{18}+\frac{1}{30}+\frac{1}{y}$ of the work per day.
The combined work rate of A, B, and C is given by $\frac19$ of the work per day.
⇒ $\frac{1}{18}+\frac{1}{30}+\frac{1}{y}=\frac{1}{9}$
⇒ $\frac{1}{y}=\frac{1}{9}-\frac{1}{18}-\frac{1}{30}$
⇒ $\frac{1}{y}=\frac{10-5-3}{90}$
⇒ $\frac{1}{y}=\frac{2}{90}=\frac{1}{45}$
⇒ $y=45$ days
Hence, the correct answer is 45 days.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
