Question

The sum of the digits of two digit number is $9$. If nine times this number is equal to twice the number obtained by reversing the order of digits of the number. Find the numbers.

• A. $18$ and $76$
• B. $18$ and $1$
• C. $98$ and $81$
• D. $18$ and $81$

Answer 1

The correct option is D $18$ and $81$

let a two digit number be $x$

sum of digits of $x$ is $9$

let units digits be $4$ and tens digits be $t$

$u+t=9$......1

Number $x$ = $u+10t$

Reverse number $x=10u+t$

$9(4+10t)=2(10u+t)$

$9u+90t=20u+t$

$11u=88t$

$u=8t$

$8t+t=9$

$t=1$

$u=8$

Number =$x=8+10=18$.

Reverse number $=x^{\prime }=1+10\times 8=81$