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19 Oct 2009, 00:34
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A pharmaceutical company received $3 million in royalties on the first$20 million in sales of and then $9 million in royalties on the next$108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next$108 million in sales?

A. 8%
B. 15%
C. 45%
D. 52%
E. 56%
[Reveal] Spoiler: OA

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19 Oct 2009, 00:57
First ratio= 3/20=15%
second ratio = (3+12)/(9+108)=15/117= 12,8%
decrease = 2,2%
2,2%/15%=15% approximately.

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19 Oct 2009, 01:26
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maliyeci wrote:
First ratio= 3/20=15%
second ratio = (3+12)/(9+108)=15/117= 12,8%
decrease = 2,2%
2,2%/15%=15% approximately.

I don't understand this calculation... why adding 9 and 108... why summing 3 and 12?

I would rather calculate the problem in this way:

3/20 -> 15%
9/ 108 -> 8.33%

8.33/15= 55.5% --> decreased by 45% approximately

The problem is a bit confusing however because at first I would have calculated in this way:

3/20 --> 15%
vs.
average royalties so far: (3+9) / (20+108) --> 12/128 --> 9.375%

--> decrease by 1-(9.375/15) --> 37.5%.

But this answer is not proposed. What do you think?

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19 Oct 2009, 01:50
The calculation should be
(3+9)/(20+108). I was confused. But you are right, the options do not include 37,5%. So the second approach (your approach) can be used.

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19 Oct 2009, 08:01
Congratulations Jgroeten, the OA is indeed C (45%). Thank you for the explanation. I couldn't figure out what the question was asking for either, but it is now clear.
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01 Nov 2010, 06:05
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(9/108)/(3/20) = 30/54 = 55,5% it means that 9/108 represents only 55,5%. Therefore a decrease of 45%.

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01 Nov 2010, 11:21
slingfox wrote:
A pharmaceutical company received $3 million in royalties on the first$20 million in sales of and then $9 million in royalties on the next$108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next$108 million in sales?

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

I'll post the answer later today.

The ratio went from $$\frac{3}{20} = \frac{9}{60}$$ to $$\frac{9}{108}$$, or $$\frac{1}{12} = \frac{5}{60}$$. That's a decrease of $$\frac{4}{60}$$. Since we went from 9 down by 4, this is a decrease of 4/9 or 44.44%. C.

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08 Nov 2010, 03:10
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slingfox wrote:
A pharmaceutical company received $3 million in royalties on the first$20 million in sales of and then $9 million in royalties on the next$108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next$108 million in sales?

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

I'll post the answer later today.

General formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent decrease can be calculated by the formula above:
$$Percent=\frac{Change}{Original}*100=$$
$$=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}$$, so the royalties decreased by approximately 45%.

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08 Nov 2010, 05:16
% = (part/whole)*100
Here, ((3/20)-(9/108)*100)/ (3/20)
Which is approx- 44.44%,

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10 Dec 2010, 07:46
Thanks for the explanation
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01 Feb 2014, 21:02
we need to find the difference between 3/20 % and 9/108 %.
had it been 3/18 and 9/108, then we would be comparing 1/6 and 1/12, which implies that royalties reduced by 50%.
Since 3/18 is little bigger than 3/20, the decrease in royalty should be little less than 50% => 45%

Question would have been lot tougher if we had multiple choice in range of 40's
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02 Feb 2014, 01:00
Ratio of first $20 m:3/20=9/60 Ratio of first$108 m:9/108=1/12=5/60

%age Change=(9/60-5/60)/(9/60) * 100
(4/9) * 100
Because 1/9= 11.11%
4/9= 44.44% ~ 45%
Ans C

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20 Sep 2014, 13:38
SunthoshiTejaswi wrote:
Bunuel wrote:
slingfox wrote:
A pharmaceutical company received $3 million in royalties on the first$20 million in sales of and then $9 million in royalties on the next$108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next$108 million in sales?

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

I'll post the answer later today.

General formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent decrease can be calculated by the formula above:
$$Percent=\frac{Change}{Original}*100=$$
$$=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}$$, so the royalties decreased by approximately 45%.

Hi Bunnuel,

is my approach correct?

instead of 108 I take 120 then actual royalitues should have been 18 but it was 9 so 50% difference.

since it was 108 the percentage should be less than 50% so it is 45%

Yes, that's correct.
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02 Sep 2017, 07:40
For $20 million sales royalties$3 million. So for $100 million sales royalty =$15 million.
For $108 million sales royalty$9 million. So for $100 million sales royalty =$12.8 million.
Percent change = (15-12.8)/15*100 = 44.46%=45%

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11 Sep 2017, 15:56
slingfox wrote:
A pharmaceutical company received $3 million in royalties on the first$20 million in sales of and then $9 million in royalties on the next$108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next$108 million in sales?

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

This is a percent decrease problem. We will use the formula percent change = (new – old)/old x 100 to calculate the final answer.

We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.

First 20 Million

royalties/sales = 3/20

Next 108 Million

royalties/sales = 9/108 = 1/12

Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percentages.

First 20 Million

royalties/sales = (3/20) x 60 = 9

Next 108 Million

royalties/sales = 9/108 = (1/12) x 60 = 5

We can plug 9 and 5 into our percent change formula:

(new – old)/old x 100

[(5 – 9)/9] x 100

-4/9 x 100

At this point we can stop and consider the answer choices. Since we know that 4/9 is just a bit less than ½, we know that -4/9 x 100 is an approximately 45% decrease.

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