Question

The sum of 2 digits number and number obtain by interchanging digits is 132. If the two digit differ by 2 find the number

Answer 1

Let us assume the x and y are the two digits of a two-digit number

Therefore, two-digit number = 10x + y and number obtained by interchanging the digit is = 10y + x

Given:

10x + y + 10y + x = 132

11x + 11y = 132

x + y = 12

x = 12 – y ------------1

Also given that:

x – y = 2 ----------2

Substitute the value of x from eqn 1 in the eqn 2

12 – y – y = 2

2y = 10

y = 5

Therefore, x = 12 – 5 = 7

Two digit number is = 10x + y = (10 * 7) + 5 = 75 
and the number obtained by interchanging the digits is = 10y + x = 10*5 + 7 = 57.

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Answer 2

let us take the tens digit be 'x' and the unit digit be 'y'
and the original no. be 10x+y and the interchanged no. will be 10y+x

according to question,
10x+