Question

The sum of the digits 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

Here's your answer

Let the digit in units place be x
Digit in tens place = 12 - x

The original number is 10(12 - x )+x

= 120 - 10x + x
= 120 - 9x ______(i)

Given,
the new number formed by reversing the digits
is greater than the original number by 18

So , by interchanging the digits, we have,

Digit in units place = 12 - x
Digit in tens place = x

The new number is 10 (x ) + 12 - x
= 10x + 12 - x
= 9x + 12 _____(ii)

Also,

the new number is greater than the original number by 18

An equation will be formed , which is as follows


$120 - 9x - 18 = 9x + 12$

$102 - 9x = 9x + 12$

Transposing the numbers , we have,

$102 - 12 = 9x + 9x$

$90 = 18x$

$x = \frac{90}{18}$
x = 5


So,
digit in units place = x = 5
Digit in tens place = 12 - x = 12 - 5 = 7

So,
the original number is 75.



Verification :
The original number = 75
Number formed by interchanging the digits = 57

Their difference = 75 - 57 = 18


So, the conditions are satisfied and our answer is correct.

Answer 2

Original number = 10x + y

When reversed,

[math]10y + x = 10x + y + 18[/math]

[math]9y = 9x + 18[/math]

[math]y = x + 2[/math]

And we know, x + y = 12

The digits are x = 5 and y = 7

Original number = 57