Question

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

• A. $1200$
• B. $11,200$
• C. $9968$
• D. $10,000$

Answer 1

The correct option is D $10,000$

If $x$ is the original population, then
$\Rightarrow x+1200-0.11(x+1200)=x-32$

$\Rightarrow 1200-0.11x-0.11\times 1200=-32$

$\Rightarrow 0.11x=1200-132+32$

$\Rightarrow x=\frac{1100}{0.11}$

$\Rightarrow x=10,000$.