Question

the sum of the digits of a two digit number is 8 if the digits are reversed the new number increased by 18 find the number

Answer 1

The number is 53.

Let the number be 10x+y.

Here x + y = 8 …(1)

10x+y - (10y+x) = 18 … (2)

(2) becomes 10x+y - 10y-x = 18 or

9x -9y = 18, or

x - y = 2 … (3)

x+y = 8 … (1). Add (1) and (3) to get

2x = 10, or x = 5. The y = 8–5 = 3

Hence the number is 53. The reverse is 35 and 53–35 = 18.