If the difference of two numbers is 3 and the difference of their squares is 39; then the larger number is:

Let the numbers are p and q.
p – q = 3 … (1)
p² – q² = 39
(p – q) (p + q) = 39 ⇒ x + y = 13 … (2)
Adding eqⁿ (1) and (2)
p + q + p – q = 16 ⇒ p = 8
∴ q = 3
Hence, 8 is the larger number.