Question

The digit in tens place of a two digit number is three times that in the units place. If the digits are reversed, the new number will be $36$ less than the original number. Find the original number. Check your solution.

Answer 1

Let units digit of the number$=x$

then tens digit $=3x$

and number $=x+10\times 3x=x+30x=31x$

On reversing the digits,

units digit $=3x$

and tens digit $=x$

then number $=3x+10x=13x$

According to the condition,

$31x-36=13x$

$\Rightarrow 31x-13x=36$

$\Rightarrow 18x=36$
$\Rightarrow x=\frac{36}{18}$
$\therefore x=2$

The original number $=31x=31\times 2=62$

Hence number $=62$

Check : Number $=62$

tens digit $=2\times 3=6$

On reversing the digit, the new number will be $=26$

$\therefore 62-26=36$ which is given.
Hence, the answer is verified