Question

The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula $C=\frac{100000p}{100-p}$. According to this estimate, how much more would it cost to remove $90$ percent of the pollutant from the pond than it would cost to remove $80$ percent of the pollutant?

• A. 500000$
• B. 100000$
• C. 50000$
• D. 10000$
• E. 5000$

Answer 1

The correct option is A 500000$

It is given, Cost $C=\frac{100000p}{100-p}$

$\Rightarrow$ Now, Cost to remove $90\%$ pollutant from pond,

$\Rightarrow$ So, here $p=90$

$\Rightarrow$ Cost to remove $90\%$ pollutant = $\frac{100,000\times 90}{100-90}=\frac{9000000}{10}=\$900000.$

$\Rightarrow$ Cost to remove $80\%$ pollutant from pond,

$\Rightarrow$ So, here $p=80$

$\Rightarrow$ Cost to remove $80\%$ pollutant = $\frac{100000\times 80}{100-80}=\frac{8000000}{20}=\$400000.$

$\therefore$ Difference between both cost = $\$900000-\$400000=\$500000$

$\therefore$ It cost $\$500000$ more to remove 90% pollutant from pond than it would cost to remove $80\%$ pollutant.