Question

The sum of digit of a two digit number is 12. If the new number formed by reversing the digits is greater
than the original number by 18, find the original number.​

Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

Question:

The sum of the digits of a 2-digit number is 12. If the digits are reversed, the new number is 18 greater than the original number. What is the original number?

Answer:

Let x represent the “tens” digit

let y represent the “ones” digit

So the original number is 10x + y

the reversed number is 10y + x

10x + y + 18 = 10y + x This is the new number is 18 more than the original

x + y =12 This is the sum of the digits is 12

Isolate x in x + y = 12 subtract y from both sides. x = 12 - y

Substitute 12-y for every x in: 10x + y + 18 = 10y + x =>

10(12-y) + y + 18 = 10y + (12-y) Distribute the 10

120 -10y + y + 18 = 10y + 12 - y Combine like terms

138 - 9y = 9y + 12 Add 9y on both sides

138 = 18y + 12 Subtract 12 on both sides

126 = 18 y divide both sides by 18

7 = y

x = 12 - y => x = 12 - 7 => x = 5

Original Number 57, new number 75.

=> Check 75 -57 = 18