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

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18 Oct 2009, 23:34

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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?

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.

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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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.

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%.

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

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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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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%

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%

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

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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%

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

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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.

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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