SSC GD 2023 PYQ — Question 44

The correct answer is option 1 i.e. $\frac{9y^2}{5}$.

Let the given numbers, a, b, and c, be in the ratio.

So, 

a : b : c

⇒ a/b = b/c

Let's assume the third proportion of 5x² and 3xy is k

So,  

⇒ 5x² : 3xy : k

⇒ 5x²/3xy = 3xy/k

⇒ 5/3y = 3y/k

⇒ k = $\frac{9y^2}{5}$