Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A group of workers having equal efficiency can complete a job in 4 days. But it so happened that every alternate day starting from the second day, 3 workers are withdrawn from the job and every alternate day starting from the third day, 2 workers are added to the group. If it now takes 7 days to complete the job, find the number of workers who started the job.
(a)4
(b)5
(c)6
(d)8
Answer
Answer (as printed): C
Explanation
Let the number of workers who started the job be $n$. Then, $n$ workers' 1 day's work $=\frac{1}{4} \Rightarrow$ 1 worker's 1 day's work $=\frac{1}{4n}$. Now, $n$ workers worked on the first day, $(n-3)$ on the 2nd day, $(n-3+2)$ i.e. $(n-1)$ on the 3rd day, ...... and so on. Thus, we have: $[n+(n-3)+(n-1)+(n-4)+(n-2)+(n-5)+(n-3)] \times \frac{1}{4n}=1 \Rightarrow 7n-18=4n \Rightarrow 3n=18 \Rightarrow n=6$. Hence, 6 workers started the job.
Explanation as extracted from the printed page; notation may be imperfect.