Question

A town's population had increased by $1200$ persons, and then its new population decreased by $11\%$. The town now has $32$ less persons than it did before the $1200$ increase. What was the original population?

• A. $10,000$
• B. $12,000$
• C. $15,000$
• D. $25,000$

Answer 1

The correct option is A $10,000$

Let x be the original population. After increase by 1200, the population is $(x+1200)$.
Let the current population decreased by 11% be y. Then
$y=(x+1200)\left\{\frac{100-11}{100}\right\}=(x+1200)(1-0.11)$
Given, this current population (y) is 32 less than x. Therefore,
$x-32=(x+1200)-0.11(x+1200)$
$-32=-0.11x+1200-132$
$0.11x=1100⟹x=10,000$
Therefore, the original population was 10,000.