If x% of 500 = y% of 300 and x% of y% of 200 = 60, then x = ?

Solution (By Examveda Team)

$$\eqalign{ & x\% {\text{ of 500 }} = y\% {\text{ of 300}} \cr & \Rightarrow \frac{x}{{100}} \times 500 = \frac{y}{{100}} \times 300 \cr & \Rightarrow 5x = 3y \cr & \Rightarrow y = \frac{5}{3}x \cr & x\% {\text{ of }}y\% {\text{ of 200}} = 60 \cr & \Rightarrow \frac{x}{{100}} \times \frac{y}{{100}} \times 200 = 60 \cr & \Rightarrow xy = 3000 \cr & \Rightarrow x \times \frac{5}{3}x = 3000 \cr & \Rightarrow {x^2} = 3000 \times \frac{3}{5} \cr & \Rightarrow {x^2} = 1800 \cr & \Rightarrow x = 30\sqrt 2 \cr} $$