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