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

Hint:
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.