Question

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

Answer 1

Let digit at ten's place be x and digit at unit's place be y.

The number formed = 10x + y

According to first condition,

x + y = 12----------------------( 1 )

The number formed after reversing the digit

= 10y + x

According to second condition,

10y + x = 18 + 10x + y

so, 10x - x + y - 10y = -18

9x - 9y = -18

Dividing both sides by 9 we get,

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

Now,

Adding equation ( 1 ) and ( 2 ) we get,

x + y = 12

+

x - y = -2

--------------------------

2x = 10

x = 5

Now,

Substituting x = 5 in equation ( 1 ) we get,

x + y = 12

5 + y = 12

y = 12 - 5

y = 7

we know that,

The original number = 10x + y

= 10 * 5 + 7

= 50 + 7

= 57

Therefore, The Original number is '57'