Question

In a two digit number, the ten's digit is three times the unit's digit. When the number of decreased by $54$, the digits are reversed. Find the number.

Answer 1

Let the digit in the unit's place be x and the digit in the ten's place be y. Then,
Number $=10y+x$

According to the given condition, we have
$y=3x$ (i)

Number obtained by reversing the digits $=10x+y$

If the number is decreased by $54$, the digits are reversed.

$\therefore$ Number $-54=$ Number obtained by reversing the digits

$\Rightarrow 10y+x-54=10x+y$

$\Rightarrow 9x-9y=-54\Rightarrow x-y=-6$ (ii)

Putting $y=3x$ in equation (ii), we get

$x-3x=-6\Rightarrow x=3$

Putting $x=3$ in $y=3x$, we get $y=9$

Hence, number $=10y+x=10\times 9+3=93$.