Minimum possible population

[Anindya Madhudor]

Can someone please show me the fastest way to solve something similar to the following?

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100

OA: D

[Anurag@Gurome]

Can someone please show me the fastest way to solve something similar to the following?

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100

OA: D

Let us assume that the minimum possible population = x
Then the maximum population = x + 10% of x = 1.1x
For x to be minimum, only one district should have minimum possible population, while the other 10 districts should have the same population, which is equal to 1.1x
So, x + 1.1*10x = 132000
12x = 132000
x = 11,000

The correct answer is D.

[Anindya Madhudor]

Thanks so much. That is much simpler than how i would have done.