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An author receives 10% of the publisher’s net receipts in royalties on

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An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 18 Apr 2018, 17:20
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An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

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An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 18 Apr 2018, 23:37
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Bunuel wrote:
An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%



For the first 10000 copies, the author receives 10% of the publisher's net receipts in royalties.
The author receives 12% of the publisher's receipts for the next 15000 copies.

If the publisher made 1$ per copy sold, the first 10000 copies would bring in \(1000$(\frac{10}{100} * 10000)\)
The next 15000 copies would bring in \(1800$(\frac{12}{100} * 15000)\)

The difference is \(\frac{1800}{15000} - \frac{1000}{10000} = \frac{3600 - 3000}{30000} = \frac{600}{30000} = \frac{1}{50}\)

As a percentage, the ratio decreases from the first 10000 to the next 15000 is \((\frac{1}{50})/(\frac{1000}{10000}) = \frac{1}{50} * \frac{10000}{1000} * 100 = 20\)

Therefore, the percentage by which the ratio decreases from first 10000 to next 15000 is \(20\)% (Option D)
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An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 19 Apr 2018, 00:31
Bunuel wrote:
An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

Method I - Lengthy arithmetic
(1) Ratios of royalty percentage to book copies sold?
First set, 10% earned on 10,000 sold: \(\frac{0.10}{10,000}\)
Next set, 12% earned on 15,000 sold: \(\frac{0.12}{15,000}\)

(2) Rewrite ratios - LCD of 30,000
\(\frac{0.10}{10,000}=\frac{0.3}{30,000}\)

\(\frac{0.12}{15,000}=\frac{0.24}{30,000}\)

(3) "By what percent does ..." = Percent change (in this case, percent decrease)

Percent change: \((\frac{New-Old}{Old}*100)\)
Calculate the change, then multiply by 100

\(\frac{(\frac{0.24}{30,000}-\frac{0.30}{30,000})}{(\frac{0.30}{30,000})}=\)

\(\frac{(-\frac{0.06}{30,000})}{(\frac{0.30}{30,000})}=(-\frac{0.06}{30,000}*\frac{30,000}{0.30})=\)

\(-\frac{0.06}{0.30}=-\frac{1}{5}=(-0.20*100) =\)

\(20\) percent decrease

Answer D

Method II. Faster arithmetic
We can treat ratios as fractions. Make these numbers more manageable. Multiply both ratios by (100*100 = 10,000). Result:
1) Decimal in both numerators moves two places to the right
2) Number in denominators loses 2 zeros, thus we have
\(\frac{10}{100}=\frac{5}{50}\)
and
\(\frac{12}{150}=\frac{4}{50}\)

Percent decrease? \(\frac{New-Old}{Old}*100\)

\(\frac{(\frac{4}{50}-\frac{5}{50})}{(\frac{5}{50})}=\frac{(-\frac{1}{50})}{(\frac{5}{50})}=(-\frac{1}{50}*\frac{50}{5})=\)

\(-\frac{1}{5}=(-0.20*100)=20\) percent decrease

Answer D
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Re: An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 23 Apr 2018, 15:52
Bunuel wrote:
An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%


The royalty percentage for the first 10,000 copies is:

0.10/10,000 = 10/1,000,000 = 5/500,000

The royalty percentage for the next 15,000 copies is:

0.12/15,000 = 12/1,500,000 4/500,000

The percent decrease is:

(4/500,000 - 5/500,000)/(5/500,000) x 100

(-1/500,000)/(5/500,000) x 100

-1/5 x 100 = -1/5 x 100 = -20 = 20 percent decrease

Answer: D
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Re: An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 05 May 2018, 06:48
First 10000 copies(A)= 10/10,000

Next 15000 copies(B)= 12/15,000

(B-A)*100/A
= 20 percent

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Re: An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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New post 01 Aug 2018, 23:00
pushpitkc wrote:
Bunuel wrote:
An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%



Hey Pushpit,

I only understood for first case author receives = $ 1000

and for second he receives = $ 1800

Other than this I am not able to understand. Please see the highlighted part.

Can you explain to me what the question is asking for. Not able to decipher what the question is asking.

Akshdeep
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Re: An author receives 10% of the publisher’s net receipts in royalties on &nbs [#permalink] 01 Aug 2018, 23:00
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