SSC CHSL 2023 PYQ — Question 54

The correct answer is option 3 i.e. 81.

Given that

$\sqrt \frac a b= \frac 8 3+ \sqrt\frac b a and (a + b) = 30$
Calculation

⇒ $\sqrt \frac a b- \sqrt\frac b a= \frac 8 3$

Squaring both sides

⇒ $\ \frac a b+ \frac b a - 2(\frac a b)(\frac b a) = \frac {64} {9}$

⇒ $\ \frac {a^2+b^2} {ab}$ = 64/9 + 2 = 82/9

Now, a + b = 30

Squaring both sides

⇒ a² + 2ab + b² = 900

⇒ 82ab/9 + 2ab = 900

⇒ 100ab = 8100

⇒ ab = 81