The sum of the digits of a $\displaystyle 2$-digit number is 14. The number obtained by interchanging its digits exceeds the given number by $\displaystyle 18$ . Find the number.

Let the required number be \(\displaystyle 10 \mathrm{x}+\mathrm{y}\) Here \(\displaystyle \mathrm{x}+\mathrm{y}=14\)---- (i) and \(\displaystyle 10 \mathrm{y}+\mathrm{x}=18+10 \mathrm{x}+\mathrm{y}\) \[\Rightarrow y-x=2 \text {---- (ii) } \] Solving (i) and (ii) to get \(\displaystyle \mathrm{x}=6, \mathrm{y}=8\) ∴ required number is 68.