Question

The sum of the digits of a two digit number is 6 and its ten's digit is twice its unit digit. Find the numbers.
A. $58$
B. $20$
C. $42$
D. $76$

Answer 1

Hint: To obtain the number we will let that it is $x$ then by using the condition given we will form equation. Then we will solve the obtain equations and put the numbers in there one’s and tens place to get our desired answer.

Complete step by step answer:
We have to find a two digit number such that sum of its digits is 6 and its ten's digit is twice its unit digit
Let the unit digit of the number be $x$.
So as it is given that its tens digit is twice as its unit digit we get,
Tens digit $=2x$
Now as the sum of the two digits is 6 we get the following equation:
$\begin{align}
  & x+2x=6 \\
 & \Rightarrow 3x=6 \\
 & \Rightarrow x=\dfrac{6}{3} \\
 & \therefore x=2 \\
\end{align}$
So we get the unit digit as 2.
The tens digit will be as below:
$\begin{align}
  & \Rightarrow 2\times 2 \\
 & \Rightarrow 4 \\
\end{align}$
Now as we know we find the number as below:
Number $=10\times \text{unit digit}+1\times \text{Tens digit}$
Number $=10\times 4+1\times 2$
Number $=40+2$
Number $=42$

So, the correct answer is “Option C”.

Note: The most common mistake in this type of question is that we take the number as $a+b$ but the correct way is to take it in $10a+b$ form as it has a representation of tens and ones place. We can check whether our answer is correct or not by seeing whether the obtained number satisfies the given condition. As in this case we got the number as 42 so the sum of its digit is 6 and its ten's digit is twice its unit digit so our answer is correct.