Freddy Friedman

2022-07-26

What single trade discount would give the same cost price as a series discount of 45%, 10%, 5%? (Note: The answer is not 60%. Round your answer to two decimal places.)

Ryan Hahn

Expert

Step 1
Lets assume price of article $=x$
After discount of 45\% price $=\frac{55}{100}x=\left(\frac{11}{20}x\right)$
Price after discount of 10% on $\frac{11}{20}x=\frac{90}{100}×\frac{11}{90}x=\frac{99}{200}x$
After discount of 5% on $\frac{99}{200}x=\frac{99}{200}x×\frac{95}{100}=\frac{19}{20}×\frac{99}{200}x$
$=\left(\frac{1881}{4000}\right)x$
$P=0.47025x$
Step 2
Total discount $=x-0.47025x$
$=0.52975x$
%discount $=\frac{0.52975x}{x}×100=52.975\mathrm{%}$

Do you have a similar question?