Question

A 2 - Digits number is twice the sum of its digit . If 63 is added to it , the digits are reversed . Find the number .​

Answer 1

Now there are two ways to do this.

Method 1:

Let the 2-digit number be xy.

Now xy can be expended as (10x + y).

10x + y = 6(x + y)

=> 4x - 5y = 0

Similarly, (x + y) + (10x + y) = 63

=> (11x + 2y) = 63

Now solving these two equations, x=5, y=4. So the number is 54.

Method 2:

The 2-digit number is a multiple of 6. And it can be concluded that it is less than 63.

So the first number that is a multiple of 6 and immediately less than 63 is 54. Just cross-check and Voila..