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

Hint: We will first consider the given data. We will let the population be \[P\] and as given that the population is increased by 1200 people so, we will form an expression with this. After the decrease of 11%, the population becomes \[P - 32\]. To find the original population, we will form an equation using the statement that the town has 32 people less than it did before the 1200 increase.

Complete step by step answer:

We will first consider the given information and we have to find the original population.
So, let the population of the town be shown by \[P\].
Now, as given in the question that the population is increased by 1200 people.
Thus, we get, \[ \Rightarrow P + 1200\]
Next, we are given that the town’s population is decreased by 11% and has 32 people less.
So, we have,
\[ \Rightarrow P - 32\]
According to the question, the new population is decreased by 11% and the town has 32 less people than it did before the 1200 increase.
So, we get,
\[
   \Rightarrow P - 32 = \left( {P + 1200} \right) - \dfrac{{11}}{{100}}\left( {P + 1200} \right) \\
   \Rightarrow P - 32 = P + 1200 - \dfrac{{11P}}{{100}} - 132 \\
   \Rightarrow \dfrac{{11P}}{{100}} = 1068 + 32 \\
   \Rightarrow P = 10000 \\
 \]
Hence, the total population is 10000.
Thus, option D is correct.

Note: We have considered the original population as \[P\]. The population is decreasing so, use all the facts given in the question and form the expression. We have simplified the expression then and find the value of the original population. While solving the expression, take all the variables on one side and constant on the other side of the expression which makes the calculation easier. As the population is increased by 1200 people so, we have added it in the \[P\]. Also, the population has 32 less people when the increased population by 1200 is added in 11% of the increased population. Do form the equation properly reading the given statement twice.