Question

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

Answer 1

Answer:

53

Step-by-step explanation:

Given: The sum of two digit number is 8

           Reversing the digit will get us number 18 less than the original.

Lets take x as tenth digit of our number and y as unit digit of our number.

As given sum of digit is 8

∴ $x+y= 8$

∴ $y= 8-x$ -       equation 1

We also know that reversing the digit will get us number 18 less than the original.

∴ $10y+x = 10x +y-18$

Now, lets put the value of y from equation 1

⇒ $10(8-x) + x = 10x+ (8-x)- 18$

⇒ $80-9x= 9x-10$

⇒ $90= 18x$

∴ $x= 5$

Next, substituting the value of x in equation 1

$y= 8-x$

⇒ $y= 8-5 = 3$

∴ $y= 3$

∴ The original number is 53, sum of the digit is 8 and if we reverse the digit of the number, we get 35, which is 18 less than the original number.