The sum of two numbers is 53 and their difference is 25. Find the numbers.

Let two whole numbers be x and y, where x y. Given, Sum of numbers = 53 ⇒ x + y = 53 .......(1) Difference of numbers = 25 ⇒ x - y = 25 ......(2) Adding equations (1) and (2), we get : ⇒ (x + y) + (x - y) = 53 + 25 ⇒ x + x + y - y = 78 ⇒ 2x = 78 ⇒ x = = 39. Substituting value of x in equation (1), we get : ⇒ x + y = 53 ⇒ 39 + y = 53 ⇒ y = 53 - 39 = 14. Hence, the numbers are 39 and 14.