A town’s 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.

Let the original population of the town be x.

The population increased by 1200.

∴ The new population of the town = x + 1200.

The new population decreased by 11%.

New quantity after decrease =

where d = decrease percent and a = original quantity.

∴ The final population of the town =

According to the given condition,

⇒ 89 (x + 1200) = 100 (x – 32) (Multiply by 100 on both

sides)

⇒ 89x + 106800 = 100x – 3200 (Removing brackets)

⇒ 89x – 100x = -3200 – 106800 (Transposing 100x to LHS

and 106800 to RHS)

-11x = -110000

⇒ x = (Transposing -11 to RHS)

x = 10000

∴ The original population of the town was 10,000.