Question

A certain two digits number is equal to five times the sum of its digits. If $9$ were added to the number, its digits would be reversed. The sum of the digits of the number is:

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is D $9$

Let the ones and tens digit of the number be $y$ and $x.$

According to question, we have

$10x+y=5(x+y)$

$\Rightarrow 5x-4y=0\dots \left(i\right)$

And,

$10x+y+9=10y+x$

$\Rightarrow 9x-9y=-9$

$\Rightarrow x-y=-1\dots \left(ii\right)$

Multiply $\left(ii\right)$ by $-4$ we get,

$\Rightarrow -4x+4y=4\dots \left(iii\right)$

Add equations $\left(i\right)$ and $\left(iii\right),$

$\left(5x-4y\right)+\left(-4x+4y\right)=0+4$

$\Rightarrow 5x-4x-4y+4y=4$

$\Rightarrow x=4$

Substitute $x=4$ in equation $\left(ii\right),$

$4-y=-1$

$\Rightarrow -y=-5$

$\Rightarrow y=5$

Thus, the sum of the digits of the number is equal to $x+y=9.$.