Question

The digit at tens place of a two digit number is two times the digit at its units place. If the digits are interchanged and added to the original number, then the result will be 66. Find the original number.

• A. 42
• B. 63
• C. 84
• D. 21

Answer 1

The correct option is A

42

Let the digit in units place be $x$.
Then, the digit in tens place will be $2x$.

So, the number will be
$(10\times 2x)+(1\times x)=20x+x=21x$

When we interchange the digits, the number will be
$(10\times x)+(1\times 2x)=10x+2x=12x$

It is given that,
$21x+12x=66$
$\Rightarrow 33x=66$
$\Rightarrow x=\frac{66}{33}$
$\Rightarrow x=2$

$\therefore$The digit in units place $=2$
The digit in tens place $=4$
The original number is $42$.

Verification:
Original number $=42$
Interchanging the digits of $42$, we get $24$.
Sum of the original number and the interchanged number is $42+24=66$.