SSC CGL 2025 PYQ — Question 57

The correct answer is Option 1 i.e. 3.

Let $a = \sqrt{5+x}, b = \sqrt{5-x}$

$\frac{\sqrt{5+x}+\sqrt{5-x}} {\sqrt{5+x}-\sqrt{5-x}} =3$

⇒ $\frac{a + b}{a - b} = 3$

⇒ a + b = 3a - 3b

⇒ 4b = 2a

⇒ a = 2b

⇒ a² = 4b²

⇒ $\left(\sqrt{5+x}\right)^2 = 4\left(\sqrt{5-x}\right)^2$

⇒ 5 + x = 4(5 - x)

⇒ 5 + x = 20 - 4x

⇒ 5x = 15

⇒ x = 3