Question

The difference between two numbers is 3 and the difference of their squares is 63. Find the greater number.

(a) 12 (b) 9 (c) 15 (d) Cannot be determined (e) None of these

Answer 1

(a) Let the larger and smaller numbers be x and y
respectively.
Then, x – y = 3   ...(i)
and, x² – y² = 63
(x + y) (x – y) = 63
(x y) =63/3 = 21   ...(ii)
From equation (i) and (ii), x = 12