Answer: Option A
:
A
Let the digit in units placebe $x$.
Then, the digit in tens placewill 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$42+24=66$.