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 taht the least populated district could have?
132,000 divided by 11 districts would give us 12,000 people on average. Also we need to keep a population of a district minimum within the condition that the population of the no district is greater than 10% of the population of the least populated district.
Hence forming equation we get
D1 + D2 + D3 + .....D11 = 132,000
Let us assume D1 is the least populated district. If we have to reduce the number of people in the district D1 to a minimum and bound to the condition, we should equally distribute the difference of the minimized population of D1 and the average population of D1 (12000) equally to the rest of the 10 districts.
Hence D2 will be equal to D3 = D4 = D5 = ....= D11. Let D2 be x and b be the population of D1
hence 10 * x + b = 132000
also we know that x \(<=\) 1.1 b. Let us take the boundary case - x = 1.1b
Hence the equation becomes 10 * 1.1 b + b = 132000
11b + b = 132000
12b = 132000 => b = 11000.
x = 12100. Hence the answer is 11,000 (D).
I hope my reasoning is sound and in understandable format.
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