The third proportional to x and x + 100 is 405, find the value of x (where x > 100)
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 125.
Third proportional to x and x + 100 is 405
So, (x + 100)² = x × 405
⇒ x × 405 = (x + 100)²
⇒ 405x = x² + 200x + 10000
⇒ x² - 205x + 10000 = 0
x = [205 ± √2025] / 2 = [205 ± 45]/2
x = 250 or 80 → (x > 100)
x = 250