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A pharmaceutical company received $3 million in royalties on

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A pharmaceutical company received $3 million in royalties on [#permalink]

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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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Re: Ratio, Percentages Problem [#permalink]

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New post 18 Oct 2009, 23:57
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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Re: Ratio, Percentages Problem [#permalink]

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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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Re: Ratio, Percentages Problem [#permalink]

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New post 19 Oct 2009, 00:50
I beg your pardon.
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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Re: Ratio, Percentages Problem [#permalink]

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New post 19 Oct 2009, 07:01
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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Re: Ratio, Percentages Problem [#permalink]

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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%.

Answer C

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Re: Ratio, Percentages Problem [#permalink]

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New post 01 Nov 2010, 10:21
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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Re: Ratio, Percentages Problem [#permalink]

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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%.

Answer: C.
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Re: Ratio, Percentages Problem [#permalink]

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New post 08 Nov 2010, 04:16
% = (part/whole)*100
Here, ((3/20)-(9/108)*100)/ (3/20)
Which is approx- 44.44%,

So Answer:- C

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Re: Ratio, Percentages Problem [#permalink]

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New post 10 Dec 2010, 06:46
Thanks for the explanation
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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 01 Feb 2014, 20:02
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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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 01 Feb 2014, 21:54
I think it wud be bit lengthy if we subtract 9/108-3/20....and then divide by 3/20

how i did..

9/108 divided by 3/20

We will get 9/108 is what of percentage of 3/20..

9/108*20/3=we will get 55% ..

this means 9/108 decrease by 45 % ..Hence C is the ans
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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 02 Feb 2014, 00:00
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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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 20 Sep 2014, 08:44
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%.

Answer: C.



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%

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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 20 Sep 2014, 12:38
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%.

Answer: C.



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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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 02 Sep 2017, 06:40
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%
Answer is 45%

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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 08 Sep 2017, 04:59
Each ratio can be derived

3:20 and 9:108.
9:108 can be converted into 1:12.
To calculate the change, we can use the following formula: (1/12)/(3/20) -1= 1/12 * 20/3 -1= 20/36 -1= (20-36)/36=-16/36=-4/9. slighlty lower than 50% so C.

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Re: A pharmaceutical company received $3 million in royalties on [#permalink]

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New post 11 Sep 2017, 14:56
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.

Answer: C
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Re: A pharmaceutical company received $3 million in royalties on   [#permalink] 11 Sep 2017, 14:56
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