Question

A towns population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.​

Answer 1

Answer:

Given :-

• A towns population Increased by 1200 people, and then this new population decreased 11%.
• The town now had 32 less population than it did before the 1200 increase.

To Find :-

• What is the original population.

Solution :-

» Let, the original population be x

» Then, the increased population will be x + 1200

» Now, the population will be decreased by 11%, so it will be 32 less than the original population which is x - 32

According to the question,

⇒ x - 32 = x + 1200 - 11% of (x + 1200)

⇒ x - 32 = x + 1200 - $\dfrac{11}{100}$ × (x + 1200)

⇒ x - x - 32 - 1200 = - $\dfrac{11}{100}$ × (x + 1200)

⇒ - 1232 = - $\dfrac{11}{100}$ × (x + 1200)

⇒ $\dfrac{11}{100}$ × (x + 1200) = 1232

⇒ x + 1200 = $\dfrac{1232 \times 100}{11}$

⇒ x + 1200 = $\sf\dfrac{\cancel{123200}}{\cancel{11}}$

⇒ x + 1200 = 11200

⇒ x = 11200 - 1200

➠ x = 10000

$\therefore$ The original population is $\large{\bf{\underline{\underline{10000}}}}$ .

Answer 2

Answer:-

Let the initial population of the town be x.

Given:

The new population increased by 1200 people.

So,

New population of the town = (x + 1200)

Also,

This new population decreased by 11% which the town had 32 people less than the original population now.

According to the question,

$\implies \sf \: (x + 1200) \times \frac{100 - 11}{100} = x - 32 \\ \\ \\ \implies \sf \:(x + 1200) \times \frac{89}{100} = x - 32 \\ \\ \\ \implies \sf \:(x + 1200) \times 89 = 100(x - 32) \\ \\ \\ \implies \sf \:89x + 106800 = 100x - 3200 \\ \\ \\ \implies \sf \:106800 + 3200 = 100x - 89x \\ \\ \\ \implies \sf \:110000 = 11x \\ \\ \\ \implies \sf \: \frac{110000}{11} = x \\ \\ \\ \implies \boxed{ \red{ \sf \:10000 = x}}$

∴ The original population of the town is 10000.