Question

In a two digit number, the digit in the unit place is twice of the digit in the tenth place. If the digits are reversed, the new number is $27$ more than the given number. Find the number.

Answer 1

Let x denote the digit in the tenth place and y denote the digit in unit place.. So, the number may be written as x y 10 + in the expanded form. (just like 35= 10(3) +5)
When the digits are reversed, x becomes the digit in unit place and y becomes the digit in the tenth place. The changed number, in the expanded form is $10y+x$.
According to the first condition, we have $y=2x$ which is written as
$2x-y=0$ (1)
Also, by second condition, we have
$(10+x)-(10x+y)=27$
That is, $-9x+9y=27\to -x+y=3$ (2)
Adding equations (1) and (2), we get x= 3.
Substituting x 3 = in the equation (2), we get y = 6.
Thus, the given number is $(3\times 10)+6=36$.