Question

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

26
35
53
62

Answer 1

original number = 53

Explanation:

In two digits number:

Let the tens place digit be x and units place digit be y.

So,

Original number = 10x + y

Number obtained after reversing the digits = 10y + x

According to the first condition:

x + y = 8.... (1)

According to the second condition:

10y + x = 10x + y - 18

10y + x - 10x - y = - 18

9y - 9x = - 18

-9(x - y) = - 18

x - y = - 18/(-9)

x - y = 2.......(2)

Adding equations (1) & (2), we find

x + y + x - y = 8 + 2

2x = 10

x = 10/2

x = 5

Plug x = 5 in equation (1), we find:

5 + y = 8

y = 8 - 5

y = 3

10x + y = 10*5 +3 = 50 + 3 = 53

Hence, original number = 53