Answer:
See explanation below
The answer by either approach is 16 years
Step-by-step explanation:
To answer your specific question , the user who responded got the ratio 25/20 as the ratio of 25000 people : 20,000 people which in fraction terms is
25,000/20,000 = 25/20
Since amount of time taken to complete the same work is inversely proportional to manpower (more people, less time, less people more time) we just divide 20 years (which is time taken for 20K people) by 25/20 to get
20 ÷ 25/20
= 20 x 20/25 (when dividing by fraction, flip the divisor and multiply
= 400/25
= 16
Another way to approach this problem is
Since time T to complete work W is inversely proportional to manpower M,
We get the proportional relationship
T ∝ 1/M
which can be written as an equation in the form:
T = k/M where k is the constant of proportionality
Cross multiplying, we get k = T· M
Given T = 20 when M = 20,000 we get k = 20 x 20,000
For M' = 25000 (people) T' = k/M'
= 20 x 20,000/25,000 = 20 x 4/5
= 16 years
