Correct Answer: ans: Larger number is 9.

Explanation:

Let, the larger number be x

And the small one is y

According to the question

x – y = 5 …………….(i)

x$^{2}$- y$^{2}$ = 65 ……………..(ii)

Now, from the equation (ii), we have

x$^{2}$- y$^{2}$ = 65

=> (x +y) (x—y) = 65

=> (x +y) (x—y) = 65

=> (x + y) x 5 = 65

x + y = 13……….. (iii)

Adding equation (iii) & (i)

Now, we get

2x = 18

x = 9