Question

In a two digit number, the tens digit is three times the units digit. When the number is decreased by $54,$ the digits are reversed. Then the number is:

• A. $36$
• B. $39$
• C. $93$
• D. $96$

Answer 1

The correct option is C $93$

Let the digit in the units place be $x$ and the digit in the ten's place by $y$. Then number $=10y+x$
According to the given condition, we have $y=3x$ -----$\left(1\right)$
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
$\Rightarrow 10y+x-54=10x+y$
$\Rightarrow 9x-9y=-54$
$\Rightarrow x-y=-6$ ---$\left(2\right)$
Putting $y=3x$ in equation $\left(2\right)$, we get $x-3x=-6\Rightarrow x=3$
Putting x = 3 in equation (1), we get y = 9 hence number = 10y + x = 10 x 9 + 3 = 93