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Arithmetic

Expert replies
by phoenix9801 » Sun Jun 27, 2010 12:22 am
Hi, can someone please help to explain the step-by-step instructions (in detail) in the most simplest way and clear to understand.

1-
A pharmaceutical company received $3 million in royalties on the first $30 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 to next $108 million in sales ?


2-
A toy regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sales, what would be the lowest possible price of a toy costing $16 before any discount?
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Source: — Problem Solving |

by albatross86 » Sun Jun 27, 2010 1:09 am
Question 1

30 million sales => 3 million royalities
Ratio of royalty to sales = 3/30 = 1/10

108 million sales => 9 million royalities
Ratio of royalty to sales = 9/108 = 1/12

So the percent drop in the ratio is expressed as : Difference in ratio divided by Original ratio * 100

= (1/10 - 1/12) / (1/10) * 100
= 1000 * (6 - 5) / 60
= 100/6
= 50/3

Approximately = 16.67%

Question 2

Discount ranges from 20% to 40%.
After discount another 25% is reduced. What is the lowest possible selling price if original price is 16$

The lowest possible price will be after MAXIMUM possible discount, i.e. 40%

First let us discount 40% from 16$ = 6.4$
So discounted price is 9.6$

Now reduce by 25% of this = 2.4$
=> Final price = Answer = 7.2$
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