Question

first a price was decreased by 12% then it was discounted again by 5% what is the percent of the total discount. From RSM

Answer 1

x = original price or 100%

so if we discount "x" by 12%, that means the new price is 100% - 12% = 88%, let's see how much is 88% of "x"

`\begin{array}ll \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{88\% of x}}{\left( \cfrac{88}{100} \right)x}\implies 0.88x`

now if we grab that new price, or the new 100%, and discount it further by 5%, what's leftover is simply 95%, because we'll be taking off 5% off of it and thus left with 100% - 5% = 95%.

so what's 95% of 0.88x?

`\begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{95\% of 0.88x}}{\left( \cfrac{95}{100} \right)0.88x}\implies 0.836x`

so the new discounted price is just 0.836x or 83.6% of our original "x".

from 100% originally to 83.6%, the difference is 16.4%, and that's the total discount.