Question

A two digit number is three more then four times the sum of its digit if 18 is added to the number the digit are reversed, find the number?

Answer 1

Let us assume x and y are the digits of a two-digit number

Therefore, the two-digit number = 10x + y and the reversed number = 10y + x

Given:

(10x + y) + 3 = 4 (x + y)

10x + y + 3 = 4x + 4y

3y – 6x = 3

y – 2x = 1 ---------1

Also given:

10x + y + 18 = 10y + x

9y – 9x = 18

y  - x = 2 ---------- 2

Subtract equation 1 from equation 2

x = 1

Therefore, y = 2 + x = 2 + 1 = 3

Therefore, the two-digit number = 10x + y = (10*1) + 3 = 13 and the reversed number = 10y + x = 31