The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?
A
15 days
B
12 days
C
5 days
D
9 days
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
The time (t) to do the work is inversely proportional to the number of workers (n).
\(\implies t \propto \frac{1}{n}\)
\(t = \frac{k}{n}\)
\(5 = \frac{k}{45} \implies k = 45 \times 5 = 225\)
\(\therefore t = \frac{225}{n}\)
For 25 men, \(t = \frac{225}{25} = 9\)
\(\therefore\) 25 men will do the work in 9 days.
Source: Myschool Past Questions Archive (Record #3351)