Question

A pharmaceutical company received $\$3$ million in royalties on the first $\$20$ million in sales of the generic equivalent of one of its products and then $\$9$ million in royalties on the next $\$108$ million in sales. By approximately, what percent did the ratio of royalties to sales decrease from the first $\$20$ million in sales?

• A. $8\%$
• B. $15\%$
• C. $45\%$
• D. $52\%$
• E. $56\%$

Answer 1

Answer: (C)

$45\%$

The ratio of royalties to sales for the first $\$20$ million in sales is $\frac{3}{20}$ and the ratio of royalties to sale for the next $\$108$ million in sales is $\frac{9}{108}=\frac{1}{12}$.

The percent decrease in the royalties to sales ratio is $100$ times the quotient of the difference in the ratios divided by the ratio of royalties to sales for the first $\$20$ million in sales or

$\frac{\frac{1}{12}-\frac{3}{20}}{\frac{3}{20}}\times 100=(\frac{1}{12}-\frac{3}{20})\times \frac{20}{3}\times 100$

$=(\frac{1}{12}\times \frac{20}{3}-1)\times 100$

$=(\frac{5}{9}-1)\times 100$

$\frac{4}{9}\times 100$

$=0.44\times 100$

$=45\%$ decrease

Hence, correct option is C.