Question

There is a number, the second digit of which is smaller that its first digit by $4$ and if the number was divided by the digits sum, the quotient would be $7$. Can you find the number?
A. $64$
B. $46$
C. $48$
D. $33$
E. $84$

Answer 1

Hint: In this question, first we will assume one digit equals a random variable and then take the second digit according to it. Then we will use the statement in the given question and we will form an equation according to that to find the value of the variable. Using the value of the variable, we can find the required number.

Complete step by step answer:
In the above question, let the first digit be $x$. According to the question, the second digit is smaller than the first digit by $4$. Therefore, the second digit will be $x - 4$.Now, we can say that if our number is “ab”, then we can also write it as $10a + b$. Therefore, we can also write our required number as $10x + x - 4$.
$ \Rightarrow 11x - 4$
Now, Sum of digits $ = x + x - 4 = 2x - 4$
Then according to the question, if the numbers were divided by the digit’s sum, the quotient would be $7$.
$ \Rightarrow \dfrac{{11x - 4}}{{2x - 4}} = 7$

Now, will do cross-multiplication here
$ \Rightarrow 11x - 4 = 7\left( {2x - 4} \right)$
$ \Rightarrow 11x - 4 = 14x - 28$
$ \Rightarrow 14x - 11x = 28 - 4$
On simplification, we get
$ \Rightarrow 3x = 24$
$ \Rightarrow x = 8$
Therefore, the first digit is $8$.
Second digit $ = x - 4 = 8 - 4 = 4$
Therefore, the required number is $84$.

Hence, the correct option is E.

Note: Do not get confused between the first digit and the second digit. First digit is that digit which is at the tenth place and the second digit is that digit which is at one’s place. Also, there should be no mistake in the calculation or we will get the wrong answer.