Question

In a two digit number, ten’s digit is twice the unit’s digit. The number formed by interchanging the digits is 36 less than the original number. Find the number.

• A. 63
• B. 42
• C. 72
• D. 84

Answer 1

The correct option is D

84

Let the units digit be $x$ $\Rightarrow$ Digit in the ten's place = $2x$

$\begin{array}{ccc}\text{Place}& 10& 1\\ \text{Digit}& 2x& x\end{array}$
The number is $10\times 2x+x=21x$
If the digits are interchanged, then
$\begin{array}{ccc}\text{Place}& 10& 1\\ \text{Digit}& x& 2x\end{array}$
The number is $10\times x+2x=12x$
According to the question, the relation between the two numbers is:-
$12x=21x–36$
$\Rightarrow$ $9x=36$
$\Rightarrow$ $x=4$
$\therefore$ The number = $21\times 4=84$.