Question

The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula${\text{C = }}\dfrac{{100000{\text{p}}}}{{100 - {\text{p}}}}$​. 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?
$
  {\text{A}}{\text{. \$ 500000}} \\
  {\text{B}}{\text{. \$ 100000}} \\
  {\text{C}}{\text{. \$ 50000}} \\
  {\text{D}}{\text{. \$ 10000}} \\
  {\text{E}}{\text{. \$ 5000}} \\
$

Answer 1

Hint – In order to find the difference in cost to remove pollutant, we first calculate the cost to remove 90 percent pollutant using the given formula, then we find the cost to remove 80 percent pollutant. Then we find the difference of both these costs to determine the answer.

Complete step-by-step answer:
Given Data,
Cost C determined by the formula, ${\text{C = }}\dfrac{{100000{\text{p}}}}{{100 - {\text{p}}}}$

To find,
The difference between the costs of removal of 90 percent pollutant and 80 percent pollutant.

The cost of removal of 90 percent pollutant is given by –
${\text{C = }}\dfrac{{100000{\text{p}}}}{{100 - {\text{p}}}}$
Here p = 90%
$
   \Rightarrow {\text{C}}\left( {{\text{ of }}90\% } \right){\text{ = }}\dfrac{{100000 \times 90}}{{100 - 90}} \\
   \Rightarrow {\text{C}}\left( {{\text{ of }}90\% } \right){\text{ = }}\dfrac{{9000000}}{{10}} \\
   \Rightarrow {\text{C}}\left( {{\text{ of }}90\% } \right){\text{ = \$ 900000}} \\
$

The cost of removal of 80 percent pollutant is given by –
${\text{C = }}\dfrac{{100000{\text{p}}}}{{100 - {\text{p}}}}$
Here p = 80%
$
   \Rightarrow {\text{C}}\left( {{\text{ of 8}}0\% } \right){\text{ = }}\dfrac{{100000 \times 80}}{{100 - 80}} \\
   \Rightarrow {\text{C}}\left( {{\text{ of 8}}0\% } \right){\text{ = }}\dfrac{{8000000}}{{20}} \\
   \Rightarrow {\text{C}}\left( {{\text{ of 8}}0\% } \right){\text{ = \$ 400000}} \\
$

Therefore, the cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant = $900000 - $400000
= $500000.
Hence Option A is the correct answer.

Note – In order to solve this type of question the key is to look closely for the data given in the question. Here in this question the formula by which the cost of removal is found out is directly given in the question so we just substitute the value to be determined.
While solving for the answer it is important to be watchful because there are many zeros in the figures and a slight error might cause us getting a wrong answer.
Identifying how much more it would cost to remove 90 percent than 80 percent pollutants is nothing but the difference in their costs of production is the key.