Question

The ten’s digit of a two digit number is 2 more than its unit’s digit. If the number is divided by the unit’s digit the quotient is 16. Find the number.
A) 64
B) 75
C) 42
D) 86

Answer 1

We will first let the unit digit be $x$ . Then, write the ten’s digit as $x + 2$. Find the number as if a number has $a$ as tens digit and $b$ as one digit, then the value of the number is, $10a + b$. Divide the number by the unit digit and is equal to 16. Solve for the value of $x$ and write the required number.

Complete step by step solution:
Let $x$ be the unit digit , then according to the question, the digit in ten’s place be $x + 2$.
If a number has $a$ as tens digit and $b$ as one digit, then the value of the number is, $10a + b$.
Similarly, the number formed by $x$ as one’s digit and $x + 2$ digit will be $10\left( {x + 2} \right) + x$, which can be simplified as, $0\left( {x + 2} \right) + x \Rightarrow 10x + 20 + x \Rightarrow 11x + 20$.
Next, we are given that if the number is divided by the unit digit, the quotient is 16.
That is when we will divide $11x + 20$ by $x$, we will get quotient as 16.
Thus,
$\dfrac{{11x + 20}}{x} = 16$
After cross-multiplying and simplifying the expression, we get,
$\dfrac{{11x + 20}}{x} = 16 \\\ 11x + 20 = 16x \\\ 20 = 16x - 11x \\\ 20 = 5x \\\ x = \dfrac{{20}}{5} \\\ x = 4 \\\$
Thus, the unit digit is 4 and the ten’s digit will be $4 + 2 = 6$.

Therefore, the number is 64.
Hence, option A is correct.

Note:
If a number has $a$ as tens digit and $b$ as one digit, then the value of the number is, $10a + b$. Many students make mistakes by taking the number as $x + y$ or $xy$, but the number will be written as $10x + y$. where, $x$ is ten’s digit and $y$ is one’s digit.