Question

Seven times a two-digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is $3$. Find the number

Answer 1

Finding the number:

Step 1. Declaring the variable

Let us assume the number at one place be $x$the number at tens place be $y$ So, the number to obtain is in the form of $10y+x$. On reversing the digits of the number, the number formed is $10x+y$

Step 2. Finding out the things mathematically.

$$\begin{gathered} 7(10y+x)=4(10x+y) \\ 70y+7x=40x+4y \\ 66y=33x \\ 2y=x \\ x=2y—–\left(i\right) \end{gathered}$$

Given that, $x-y=3$

Step 3. Substitution of values

On substituting $x=2y$ in the above equation we get

$$\begin{gathered} 2y-y=3 \\ y=3 \\ x=2y \\ =2\left(3\right) \\ =6 \end{gathered}$$
Hence, the required number is $36$ on reversing digit is $63$.