Question

the sum of digit of a two digit number is 11 if he is added to the number its digits are reversed find the number​

Answer 1

Correct Question:-

The sum of the digits of a two digit number is 11. If 9 is added to the number its digits are reversed. Find the number.

Answer:-

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

The number = 10x + y

Given:

Sum of the digits = 11

→ x + y = 11 -- equation (1)

And,

If 9 is added to the number its digits are reversed.

→ Original number + 9 = Reversed number

→ 10x + y + 9 = 10y + x

→ 10x + y - 10y - x = - 9

→ 9x - 9y = - 9

→ (x - y) * 9 = - 9

→ x - y = - 9/9

→ x - y = - 1 -- equation (2)

Add equations (1) & (2).

→ x + y + x - y = 11 + ( - 1)

→ 2x = 10

→ x = 10/2

→ x = 5

Putting the value of x in equation (1) we get,

→ x + y = 11

→ 5 + y = 11

→ y = 11 - 5

→ y = 6

The number = 10 * 5 + 6 = 50 + 6 = 56

Therefore, the required number is 56.