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 54, find the original number. Check your
solution.​

Answer 1

Answer:

Let one digit be x

then, another digit = 12-x

if x is at tens place and (12-x) is at one's place

then , original number = 10x+12-x

= 9x+12

when number is reversed, (12-x) will be at tens and x will be at one's place.

then ,the number = 10(12-x)+x

= 120-10x+x

= 120-9x

A/Q

(120-9x)-(9x+12)=54

or, 120-9x-9x-12 =54

or, 108-18x = 54

or, -18x = 54 -108

or, -18x = -54

or, x = -54/-18

or, x = 3

Since, one digit is 3

Another digit = 12 -3

=9

therefore , Original number = 39

Checking solution :

Original number = 39

Number on reversing original number = 93

Difference between two numbers :

= 93 - 39 = 54

Checked