Question

The $2$ digit number which becomes ${\left(\frac{5}{6}\right)}^{th}$ of itself when its digits are reversed. Find out the number when the difference of the digits is $1$.

• A. $45$
• B. $54$
• C. $36$
• D. None of these

Answer 1

The correct option is B $54$

The number becomes $\frac{5}{6}$ of itself on reversing that is the reversed number is less than the original number.
$\therefore$ the tens digit in the original number is greater than the unit place digit.

Let the number be $10x+y$, then $(x-y)=1$ ....given

$\Rightarrow x=(y+1)$ ....(1)

Again $\frac{5}{6}(10x+y)=10y+x$

$\Rightarrow 44x=55y$

$\Rightarrow 4x=5y$ ....(2)

Substituting for $x$ from (1), we get

$4(y+1)=5y$

$\Rightarrow y=4$

$\Rightarrow x=y+1=5$

$\therefore$ the two digit number is $54$.