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 $1200$ increase. Find the original population.

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Solution

Let original population $= x,$ given it increased by $1200.$

New population $= x + 1200.$ This new population decreased by $11$ %

Final population $=$ New population $- 11$ % of New population
$= (x + 1200) \times (1 - \frac{11}{100})$
Final Population
$= (x + 1200) \times (1 - \frac{89}{100})$
Given Final population is $32$ less than original population.
$\Rightarrow (x + 1200) \times (1 - \frac{89}{100}) = x - 32 89 x + 106800 = 100 x - 3200 11 x = 110000 x = 10000$
$∴$ Original population $= 10000$

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