the difference between two numbers is 3 and the difference between their squares is 63. Which is the larger number ?

Answer: Option B

Let the number be x and y
Then,
$$x^2-y^2=63\&x-y=3$$
On dividing, we get: x + y = 21
Solving x + y = 21 and x - y = 3,
We get: x = 12 and y = 9
∴ Larger number = 12