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 2 answer key released | 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 “”.
Upcoming Exams
Trending Articles around SSC CHSL
