The difference between the two numbers is 50

let the numbers be x+y

∴ y-x=50

y=x+50

$$\begin{gathered} =\frac{x}{y}=\frac{3}{8} \\ =x=\frac{3y}{8} \\ =y-\frac{3y}{8}=50 \\ =8y-\frac{3y}{8}=50 \\ =5y=400 \\ \therefore x=y-50=30 \end{gathered}$$

The largest number is 80 and smallest number is 30.

Hence, Option A is correct.