Question

the sum of digits of a 2-digit number is 11. the number obtained interchanging the digits exceeds the original number by 27 find the number

Answer 1

Let the one's digit number be $\textbf{y}$ and tens digit number be $\textbf{x}$.

Original number = 10x + y

Number obtained by interchanging the digits -

=> 10y + x

A/q

$\textbf{x + y = 11}$

Also,

10y + x = 10x + y + 27

On solving further,

10y - y + x - 10x = 27

9y - 9x = 27

9(y - x) = 27

$\textbf{y - x = 3}$

Add both the equations, we get

2y = 14

$\large\textbf{y = 7}$

Now,

y - x = 3

7 - x = 3

$\large\textbf{x = 4}$