Question

The sum of two digit number and the number obtained by interchanging the digits of the number is 121. If the digits of the number differ by 3, find the number.

Answer 1

Let the tens digit of the number be x and the units digit be y.
So, the number is 10x + y.
The number obtained by interchanging the digits will be 10y + x.
According to question, we have
10x + y + 10y + x = 121
⇒ 11x  + 11y = 121
⇒  11( x + y ) = 121
⇒  x + y = 11                       ...(1)
And, 
x - y = 3                               ...(2)

Adding (1) and (2), We get
∴ 2x = 14
x = 7

∴ y = 11 - x = 11 - 7 = 4
Hence, the number is 74.