Question

The ones digit of a 2-digit number is twice the tens digit. When the number formed by reversing the digits is added to the original number, the sum is 99. Find the original number

Answer 1

Let the two digit number is x and y and the number is xy

y is digit at unit's place

x is digit at ten's place

$\Rightarrow$ Number can be written as = $10x+y$

According to the conditions : $y=2x$ ___ (1)

and

$(10x+y)+(10y+x)=99$

$\Rightarrow 11x+11y=99$

$\Rightarrow x+y=9$ (dividing by 11)

Now $x+2x=9$ (from (1))

$\Rightarrow 3x=9$

$\Rightarrow x=9/3=3$

$y=2x=6$

$\Rightarrow$ Number is 36