Question : The sum of two numbers is 680. If the bigger number is decreased by 15% and the smaller number is increased by 15%, then the resultant numbers are equal. Find the smaller number.
Option 1: 307
Option 2: 285
Option 3: 289
Option 4: 304
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Correct Answer: 289
Solution :
Let the bigger number be $x$.
Smaller number = $680 - x$
According to the question,
$x(1 - 15\%) = (680 - x)(1 + 15\%)$
⇒ $\frac{x}{(680 - x)} = \frac{23}{17}$
⇒ $17x = 23 × 680 - 23x$
⇒ $40x = 23 × 680$
⇒ $x = 23 × 17$
⇒ $x = 391$
So, the smaller number = 680 – 391 = 289
Hence, the correct answer is 289.
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