Comment

(This is really the solution.)

  1. Let P be the original price.

  2. Then, P - ${\frac{{% d}}{{100}}}$P = p.

  3. Hence P$\left(\vphantom{ 1-\frac{% d}{100}}\right.$1 - ${\frac{{% d}}{{100}}}$$\left.\vphantom{ 1-\frac{% d}{100}}\right)$ = p.

  4. This is P$\left(\vphantom{ 1-\frac{1}{100}d}\right.$1 - ${\frac{{1}}{{100}}}$d$\left.\vphantom{ 1-\frac{1}{100}d}\right)$ = p.

  5. We get P = ${\frac{{% p}}{{% 1-\frac{1}{100}d}}}$ = ${\frac{{p}}{{1-\frac{1}{100}d}% }}$.