Question

The sum of a number of two digit and of the number formed by reversing the digit is 110 and different of the object is 6 find the number.​

Answer 1

Answer:

82

Step-by-step explanation:

Let the original number be ( 10x + y )

Then the number formed by reversing the digits is ( 10y + x )

Given that the sum of the two numbers is 110.

⇒ 10x + y + 10y + x = 110

⇒ 11x + 11y = 110

Dividing by common factor 11 we get,

⇒ x + y = 10   ...( Eqn 1 )

Also given that, the difference of the digits is 6.

⇒ x - y = 6   ...( Eqn 2 )

Therefore adding  Eqn 1 and Eqn 2 we get,

⇒ x + y + x - y = 10 + 6

⇒ 2x = 16

⇒ x = 16/2 = 8

Therefore y = x - 6

⇒ y = 8 - 6 = 2

Therefore the original number is 10x + y.

⇒ 10 ( 8 ) + 2 = 80 + 2 = 82

Hence the original number was 82.