Chapter 9, Problem 8MPS

To determine

To Find: The two digits number.

Answer to Problem 8MPS

  $72$

Explanation of Solution

Given: The tens digit of a two-digit number is 1 more than 3 times the units digit. Subtracting 45 from the number reverses it.

Let two digit number be $10x+y$

Where, $x$ represents tens digit and $y$ represent unit digit.

According to question,

The tens digit of a two-digit number is 1 more than 3 times the units digit.

  $x=3y+1\mathrm{...}\left(i\right)$

Subtracting 45 from the number reverses it.

  $\begin{array}{c}10x+y-45=10y+x\\ 9x-9y=45\\ x-y=5\mathrm{...}\left(ii\right)\end{array}$

From $\left(i\right)\text{ and }\left(ii\right)$

  $\begin{array}{c}3y+1-y=5\\ 2y=4\\ y=2\end{array}$

Put $y=2$ in ( i )

  $\begin{array}{l}x=3\left(2\right)+1\\ x=7\end{array}$

Hence, the original number is 72