If ( x - 24 ) ( 75 + 50 ) 75 - 50 = 1 then the value of x is = ?

Answer: Option B

$$\begin{array}{rl}& \frac{\left(x-\sqrt{24}\right)\left(\sqrt{75}+\sqrt{50}\right)}{\sqrt{75}-\sqrt{50}}\text{ = 1 }\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{\sqrt{75}-\sqrt{50}}{\sqrt{75}+\sqrt{50}}\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{{\left(\sqrt{75}-\sqrt{50}\right)}^2}{75-50}\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{75+50-2\sqrt{75}\sqrt{50}}{25}\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{125-2\times 5\sqrt{3}\times 5\sqrt{2}}{25}\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{125-50\sqrt{6}}{25}\\ & \Rightarrow \left(x-\sqrt{24}\right)=\frac{25\left(5-2\sqrt{6}\right)}{25}\\ & \Rightarrow x-2\sqrt{6}=5-2\sqrt{6}\\ & \Rightarrow x=5\end{array}$$