SSC CGL 2025 PYQ — Question 75

The correct answer is option 1 i.e. $\frac{56}{17}$.

Let a = √(7 + x) and b = √(7 - x)

$\frac{\sqrt{7+x} + \sqrt{7-x}}{\sqrt{7+x} - \sqrt{7-x}} = 4$

⇒ (a + b)/(a - b) = 4

⇒ a + b = 4a - 4b

⇒ 5b = 3a

⇒ a/b = 5/3

Substitute back: $\frac{\sqrt{7+x}}{\sqrt{7-x}} = \frac{5}{3}$

⇒ $\frac{7+x}{7-x} = \frac{25}{9}$

⇒ 63 + 9x = 175 - 25x

⇒ 34x = 112

⇒ x = 112/34 = 56/17