Question

A town’s population increased by 1200 people, and then decreased 11 percent. The town had 32 less people than it did before the 1200 increase. Find the original population.
A) 10000
B) 11000
C) 12000
D) 13000

Answer 1

Hint: First assume that the original population of the town is x. Now form an equation according to the conditions given in the question and then solve it to find the value of x.

Complete step-by-step answer:
Let us assume that the original population of the town is x.
Now it is given in the question that the population increased by 1200 people.
So the increased population will be x+1200.
After increasing, the population decreased by 11 percent.
11 percent of x+1200 will be,
$\left( x+1200 \right)\times \dfrac{11}{100}$
Therefore the population becomes,
$\left( x+1200 \right)-\left( x+1200 \right)\times \dfrac{11}{100}$
Now it is given in the question that the town had 32 less people than it did before the 1200 increase.
Therefore,
$\left( x+1200 \right)-\left( x+1200 \right)\times \dfrac{11}{100}=x-32....(1)$
Now we will solve the equation (1) to find out the value of x.
Let us multiply both sides of the equation by 100.
$\Rightarrow 100\left( x+1200 \right)-11\left( x+1200 \right)=100\left( x-32 \right)$
$\Rightarrow 89\left( x+1200 \right)=100x-3200$
$\Rightarrow 89x+106800=100x-3200$
Now we will take all the terms with x on the left hand side and all the constant terms on the right hand side. Therefore,
$\Rightarrow 89x-100x=-3200-106800$
$\Rightarrow -11x=-110000$
Now we can cancel out the negative terms from both sides.
$\Rightarrow 11x=110000$
Now we will divide both sides of the equation by 11. Therefore,
$\Rightarrow x=\dfrac{110000}{11}$
$\Rightarrow x=10000$
Hence, the original population is 10000 people.
Therefore, option (A) is correct.

Note: Alternatively, we can solve this problem by cross checking the options. Only option (A) is satisfying all the conditions given in the question. Therefore, option (A) is correct.