Question

The sum of a two digit number and the number obtained by interchanging the digits is 132. if the two digits differ by 2, find the number(s)

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.

Answer 2

Answer:

Step-by-step explanation:

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