Sum of two numbers is 384. HCF of the numbers is 48. The difference of the numbers is = ?

Answer: Option C

HCF = 48
Let number are 48x and 48y respectively
$$\begin{array}{rl}& \Rightarrow 48x+48y=384\\ & \left(x+y\right)=\frac{384}{48}=8\end{array}$$
So, possible pairs of co-prime number are (1, 7) (3, 5)
numbers are (48, 336) or (144, 240)
∴ difference between numbers is = 336 - 48
= 288 and 240 - 144 = 96