Question

The sum of a two digit number and the number obtained by reversing the digits is 121. If the difference between the digits is 3, find the number.

Answer 1

The number is 47
47 reversing the digits= 74
47+74= 121
Difference 7-4=3

Answer 2

$\pink{\boxed{\huge Answer}}$

The number can be written in the form 10*x + y, where y is the unit digit and x is the 10’s digit.

For instance: 38 is 3*10 + 8, and x=3 and y=8.

Reversing the order of digits, we get 10*y + x.

We know that the number plus the number obtained by reversing the digits is 121.

Or 10x + y + 10y + x = 121.

Or 11x + 11y = 121

We also know that the digits differ by 3. So, x - y = 3 (It could also be y - x = 3)

Multiplying this equation by 11, we get 11x - 11y = 33.

Adding the two equations, we get:

11x + 11y + 11x - 11y = 121 + 33.

or 22x = 154 or x = 7 and therefore y = x -3 = 4.

Therefore the number is 74.

Remember that we could also have y -x =3, in which case the number is 47, which gives us the same result.