Question

The ten's digit of a two digit number exceeds its unit's digit by \[4\]. If the ten's digit and the unit's digit are in the ratio \[3:1\], find the number.
A.\[62\]
B.43
C.55
D.75

Answer 1

Hint: We will assume the two digits to be two separate variables. The method to form a number where the tens digit is a and the units digit is b is \[10a + b\].

Complete step-by-step answer:
From the given question, we get to know that the difference between the tens digit and the units digit is \[4\]. Also, the tens digit and the units digit are in the ratio \[3:1\].
Now, let us assume the tens digit to be \[x\] and the units digit to be \[y\].
So, the number will be \[10x + y\].
Now, according to the question, we know
\[x - y = 4......(1)\]
And \[x:y = 3:1\]
We will now cross multiply the ratio.
We get,
\[
  x:y = 3:1 \\
   \Rightarrow \dfrac{x}{y} = \dfrac{3}{1} \\
   \Rightarrow x = 3y \\
   \Rightarrow x - 3y = 0......(2) \\
\]
We will now simultaneously solve (1) and (2),
\[x - y = 4 \Rightarrow x = 4 + y\]
Substituting the above equation in (2), we get
\[
  x - 3y = 0 \\
   \Rightarrow 4 + y - 3y = 0 \\
   \Rightarrow 4 - 2y = 0 \\
   \Rightarrow 4 = 2y \\
   \Rightarrow y = \dfrac{4}{2} = 2 \\
\]
Therefore, the units digit\[y = 2\].
Now, substituting \[y = 2\]in (1), we get
\[
  x - y = 4 \\
   \Rightarrow x - 2 = 4 \\
   \Rightarrow x = 4 + 2 \\
   \Rightarrow x = 6 \\
\]
Therefore, the tens digit \[x = 6\].
Therefore, the required number is \[10x + y = 10 \times 6 + 2 = 60 + 2 = 62\].
Thus, the answer is option A.

Note: In these types of questions, we need to remember that when a two digit number is formed, \[10\] has to be multiplied to the tens digit. A two digit number is the sum of \[10\] multiplied to the tens digit and the units digit.