Question

A number consists of two digits whose sum is 8. If 18 is added to the number its digits are reversed. Find the number.

Answer 1

$\begin{array}{l}\text{Let}\mathit{\text{x}}\text{be the digit in the units place.}\\ \text{Sum of the units and tens digits}=8\\ \text{Then, tens digit}=(8-x)\\ \therefore \mathrm{T}\text{he number is 10}(8-x)+x.\\ \text{Now, 10}(8-x)+x+18=10x+(8-x)\\ \Rightarrow \text{80}-10x+x+18=10x+8-x\\ \Rightarrow \text{98}-9x=9x+8\\ \Rightarrow \text{18}x=90\\ \Rightarrow x=5\\ \text{i.e., tens digit=}(8-5)\text{=3}\\ \therefore \mathrm{Required}\text{number=10}(8-5)\text{+5=10}\times \text{3+5=35}\end{array}$