Question

The ten's digit of a two digit number is thrice the unit digit. The new number obtain interchanging the digits is $54$ less than the Original number. Find the original number.

Answer 1

Let say 'x' is digit in one's place so $3x$ is digit in tens place.

So number is $10.3x+x=31x$

Now if interchanging the position of digit new number is $10x+3x=13x$

As given now number is less than $54$ from old number.

$31x-54=13x$

$\Rightarrow 31x-13x=54$

$\Rightarrow 18x=54$

$\Rightarrow x=54/18$

$\Rightarrow x=3$

So, the number is $\mathrm{10.3.3}+3=93$

$\therefore$ The original number is $93$.