Chapter 5.2, Problem 35E

To determine

To find: The original number.

Answer to Problem 35E

The required original number is $47$ .

Explanation of Solution

Given information: The sum of the digits of a two digits number is $11$ and when digits are reversed, the number increases by $27$ .

Calculation: Let x be the units digit and y be tens digit.

Hence, according to the question,

  $\begin{array}{l}y+x=11\\ y=11-x\mathrm{...}\left(1\right)\end{array}$

When the number get reversed,

  $10x+y=10y+x+27\mathrm{...}\left(2\right)$

Put $y=11-x$ in equation (2),

  $\begin{array}{l}10x+\left(11-x\right)=10\left(11-x\right)+x+27\\ 10x+11-x=110-10x+x+27\\ 18x=126\\ x=7\end{array}$

Put $x=7$ in equation (1),

  $\begin{array}{l}y=11-x\\ y=11-7\\ y=4\end{array}$

Therefore, the original number is $47$ and its reversed is $74$ that is greater by 27 than $47$ .