Question

The sum of the digits of a two digit number is $8$. The digits of number get reversed when $18$ is subtracted from the number. Find the original number.

• A. $32$
• B. $53$
• C. $62$
• D. $71$

Answer 1

Answer: (B)

$53$

Let $x=$ the ${10}^{\prime }$s digit and $y=$ be the unit digit

$\therefore 10x+y=$original number

The sum of the digits of a two digit number is $8$.

$\Rightarrow x+y=8$.....(1)

The digits of number get reversed when $18$ is subtracted from the original number.

$\therefore$ Reversed digit $=$ original number $-18$

$\Rightarrow 10y+x=10x+y-18$

$\Rightarrow 10y-y=10x-x-18$

$\Rightarrow 9y=9x-18$

$\Rightarrow y=x-2$

Put the value of $y$ in (1)

$\Rightarrow x+x-2=8$

$\Rightarrow 2x=8+2$

$\Rightarrow 2x=10$

$\Rightarrow x=\frac{10}{2}=5$

$\Rightarrow x+y=8$

$\Rightarrow 5+y=8$

$\Rightarrow y=8-5$

$\Rightarrow y=3$

$\therefore$ Original number $=53$