Question

In a two-digit number, the digit at tens place is double the digit at units place. If the digits of the number are interchanged, the new number so formed is $27$ less than the original number. Find the original number.

• A. $55$
• B. $60$
• C. $63$
• D. $68$

Answer 1

The correct option is C $63$

Let, the digit at tens place be $x$ and the digit at units place be $y$ in the original number.
Then the original number $=10+y$, and the new number obtained by interchanging the digits $=10y+x$.
By the data, the digit at tens place is double the digit at units place.
$\therefore x=2y$
$\therefore x-2y=0$ ............. (1)
Again, new number $=$ original number - 27
$\therefore 10y+x=10x+y-27$
$\therefore 10y+x-10x-y=-27$
$\therefore -9x+9y=-27$ $\therefore x-y=3$ ........... (2)
Subtracting eq. (1) from eq. (2),
$x-y=3$
$x-2y=0$
- + -
__________
$y=3$
Substituting $y=3$ in $x-2y=0$
$\therefore x-2\left(3\right)=0$
$\therefore x-6=0$
$\therefore x=6$
Then, the original number $=10x+y=10\left(6\right)+3=63$
Hence, the original number is $63$.