Question

The sum of digits of a two-digit number is 7. If th digits are reversed, the new number decreased by 2 equals twice the original number. Find the number.

Answer 1

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

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

Given:

x + y = 7

y = 7 – x -----------1

also given:

10y + x -2 = 2 (10x + y)

10y + x -2 = 20x + 2y

8y – 19x = 2

8 (7 – x) -19x = 2

56 – 8x -19x = 2

27x = 54

x = 2

Therefore, y = 7 – x = 7 – 2 = 5

The two-digit number = 10x + y = (10 * 2) + 5 = 25