Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

The sum of the digits of a two-dlgit number is $9$. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number

• A. None of these
• B. Number is $18$
• C. Number is $36$
• D. Number is $81$

Answer 1

Answer: (B)

let the unit digit $=x$
Ten digit $=y$
Sum of two digits are $9$
$\therefore x+y=9$ ........(1)
Number will $10$ times the tens digit $+$ unit times the unit digit
$\therefore$ Number $=10y+x$
The number obtained by reversing the order of digit
$\Rightarrow 10x+y$
According to the second condition, we have
$9(10y+x)=2(10x+y)$
$\Rightarrow 90y+9x=20x+2y$
$\Rightarrow 88y-11x=0$
Divide by $11$,
$\Rightarrow 8y-x=\mathrm{0.......}$ (2)
Adding both equation,
$\Rightarrow 9y=9$

$\Rightarrow y=1$
Put $y=1$ in (1)
$\Rightarrow x+1=9\Rightarrow x=8$
Hence, the original number is $10y+x=10\times 1+8=18$.