Question

now?
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
​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• A town's population increased by 1200 people

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• Then this new population decreased 11%

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• The town now had 32 less people than it did before the 1200 increase

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$\large\underline{\red{\bf To \: Find :-}}$

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• Original population

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the total population be "x"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\underline{\bold{\texttt{Case 1 :}}}$

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Town's population increased by 1200 people

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New population

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➠ x + 1200

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$\underline{\bold{\texttt{Case 2 :}}}$

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Also given that new population decreased 11%

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New population

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➠ $\sf (x + 1200) - \dfrac { 11 } { 100 } \times (x + 1200)$

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Given that the town now had 32 less people than it did before the 1200 increase

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So,

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

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➜ $\footnotesize{ \sf \dfrac { 100x + 120000 - 11x - 13200 + 3200 } { 100 } = x }$

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➜ $\sf \footnotesize{ 100x = 100x + 120000 - 11x - 13200 + 3200 }$

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➜ $\sf \footnotesize{ 11x = 120000 - 13200 + 3200 }$

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➜ $\sf \footnotesize{ 11x = 123200 - 13200 }$

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➜ $\sf \footnotesize{ 11x = 110000 }$

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➜ $\sf \footnotesize{ x = \dfrac { 110000 } { 11 }}$

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➨ $\bf \footnotesize{ x = 10000 }$

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• Hence the original population of the town was 10000

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