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The income of a broker remains unchanged though the rate of commission

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The income of a broker remains unchanged though the rate of commission [#permalink]

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New post 15 Oct 2017, 06:14
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Question Stats:

78% (00:27) correct 22% (03:39) wrong based on 9 sessions

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The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is:

A. 8%

B. 1%

C. 20%

d. 80%

E. 5%
[Reveal] Spoiler: OA

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The income of a broker remains unchanged though the rate of commission [#permalink]

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New post 15 Oct 2017, 06:34
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zahinsarwar wrote:
The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is:

A. 8%

B. 1%

C. 20%

d. 80%

E. 5%


Let \(S_1\) be initial sales and \(S_2\) be sales after increase in commission %. We need to find \(\frac{S_1-S_2}{S_1}\)

Given \(S_1*4\)%\(=S_2*5\)% \(=> \frac{S_2}{S_1}=\frac{4}{5}\). subtract both sides of the equation from \(1\) to get

Or, \(1-\frac{S_2}{S_1}=1-\frac{4}{5}\)

\(\frac{S_1-S_2}{S_1}=\frac{1}{5} => 20\)%

Option C

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Re: The income of a broker remains unchanged though the rate of commission [#permalink]

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New post 15 Oct 2017, 06:48
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Here,
let be the value of business 100
and, the percentage of slump of business is x
So, according to question,
100 * 4/100 = (100-x) * 5/100
4 = (100-x)/20
80 = 100 -x
100 -x = 80
- x = 80-100
-x = -20
x= 20

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Re: The income of a broker remains unchanged though the rate of commission [#permalink]

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New post 15 Oct 2017, 07:50
zahinsarwar wrote:
The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is:

A. 8%

B. 1%

C. 20%

d. 80%

E. 5%


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Re: The income of a broker remains unchanged though the rate of commission   [#permalink] 15 Oct 2017, 07:50
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