There are three towns of A, B and C in a certain district.
The ratio of the area of the town is A : B : C = 3 : 5 : 2, the ratio of the population is A : B : C = 5 : 4 : 3.
If A town merges with B town, there is a new town of the population density of 7065 people per 1 km2.
If A town merges with B town and C town to be a new town, how many people per 1 km2 is the population density?
Answer
7536 people
Solution
Population density is calculated by population / area.
When the ratio of the population and the area of three towns is identified, population density can be calculated with a ratio.
That is, when A and B merge, the area is 3 + 5 = 8 and the population is 5 + 4 = 9.
Thus, the population density is 9/8 and 9/8 is equivalent to 7065 people.
When A, B, and C merge, the area is 3 + 5 + 2 = 10 and the population is 5 + 4 + 3 = 12.
The population density is 12/10 = 6/5.
The ratio of population density between 6/5 and 9/8 is set to 16 : 15.
The population density per 1 km2 is 7065 × 16 / 15 = 7536 people.
