Question

A number consists of two digits. The digit at the tens place is twice that of the digit at the unit. If $18$ is subtracted from the number, the digits are reversed. Find the number.

Answer 1

Let the one's place be y and tens digit be x.

then, Number = 10x + y.

$\therefore$ Given, (x) = 2y $\therefore 5x=2y\cdots \left(i\right)$

But, if 18 is subtracted, then, number gets reversed

ie. 10y + x.

$\therefore (10x+y)-18=10y+x$

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

$\Rightarrow 10x-x+y-10y-18=0$

$\Rightarrow 9x-9y-18=0$

$\Rightarrow x-y-2=0$ Putting $[y=\frac{5x}{2}]$

$\Rightarrow x-\frac{5x}{2}-2=0$

$\Rightarrow 2x-x-2=0$ $\therefore y=\frac{x}{2}$ y = 1

$\Rightarrow x=2$

$\therefore$ Number = 21