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# The average (arithmetic mean) monthly income of four workers

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The average (arithmetic mean) monthly income of four workers [#permalink]

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25 Feb 2013, 10:09
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The average (arithmetic mean) monthly income of four workers is \$2,200. After one worker’s income increases by 25 percent the new average income is \$2,400. What was the original income of the worker whose monthly income increased?

A. \$800
B. \$1,200
C. \$2,400
D. \$3,200
E. It cannot be determined from the information given .
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Feb 2013, 02:37, edited 2 times in total.
Edited the question.

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Re: The average (arithmetic mean) monthly income of four worker [#permalink]

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25 Feb 2013, 10:54
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Let the income of the 3 workers which doesn't change be x1,x2,x3. Let the income s increase by 25%. Thus,

Initially, x1+x2+x3+s= 8800

And later, x1+x2+x3+1.25s = 9600

Subtracting both of them,

0.25s = 800

Thus, s = 3200.

D.
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Re: The average (arithmetic mean) monthly income of four worker [#permalink]

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25 Feb 2013, 10:56
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a+b+c+d=4*2.2 => b+c+d=4*2.2-a

1.25a+b+c+d=4*2.4

1.25a+ (4*2.2-a)=4*2.4
0.25a=4*(2.4-2.2)

(1/4)a=4*.02
a=3.2

ans is D
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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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26 Feb 2013, 02:44
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Expert's post
thinktank wrote:
The average (arithmetic mean) monthly income of four workers is \$2,200. After one worker’s income increases by 25 percent the new average income is \$2,400. What was the original income of the worker whose monthly income increased?

A. \$800
B. \$1,200
C. \$2,400
D. \$3,200
E. It cannot be determined from the information given .

Increase in total income was 200*4=\$800, we know that this increase was 25% (1/4th) of the workers original income, thus his/her original income was 800*4=\$3,200.

Hope it's clear.
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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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09 Apr 2014, 12:26
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The average (arithmetic mean) monthly income of four workers [#permalink]

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14 Sep 2015, 03:33
Hello.

When the question refers to the "original income", it means before the increase of 25% or just the 100% after the increase? Why the question couldn't be like "What is the actual income of the worker who's income increased?" or something like that?

The question is correct, I thought that the monthly salary would be an integer and not something like 1886.67. So the original is 3200 and the increase would take it to 4000. All clear!

Best!
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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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14 Sep 2015, 04:39
snfuenza wrote:
Hello.

When the question refers to the "original income", it means before the increase of 25% or just the 100% after the increase? Why the question couldn't be like "What is the actual income of the worker who's income increased?" or something like that?

The question is correct, I thought that the monthly salary would be an integer and not something like 1886.67. So the original is 3200 and the increase would take it to 4000. All clear!

Best!

What do you mean by your text in red above?

The question is clear as stated. Lets say the worker was earning 100\$ before the 25% increase. With 25% increase, his new salary will be come = 125\$. Thus when I ask you the "original salary" it will always mean that I want you to say 100\$ and not 125\$.
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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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14 Sep 2015, 10:07
Engr2012 wrote:
snfuenza wrote:
Hello.

When the question refers to the "original income", it means before the increase of 25% or just the 100% after the increase? Why the question couldn't be like "What is the actual income of the worker who's income increased?" or something like that?

The question is correct, I thought that the monthly salary would be an integer and not something like 1886.67. So the original is 3200 and the increase would take it to 4000. All clear!

Best!

What do you mean by your text in red above?

The question is clear as stated. Lets say the worker was earning 100\$ before the 25% increase. With 25% increase, his new salary will be come = 125\$. Thus when I ask you the "original salary" it will always mean that I want you to say 100\$ and not 125\$.

Sorry, yes, I got confused and now I understand it.

Thanks!
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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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10 Dec 2016, 09:09
Great Question.
Two methods to solve this one.
Method 1->
Sum (1) => 8800
Sum(2)=>9600
Increase => 800
Hence 25 percent of income =800
So the original income must be 3200

Method 2-->
Lets use fundamentals here.
Mean 1=> 2200
Mean 2=> 2400
Hence the increased amount will be 800.
So 25 percent of the income will be 800
Hence 100 percent of the income => 800*4=> 3200

Hence D

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Re: The average (arithmetic mean) monthly income of four workers [#permalink]

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10 Dec 2016, 11:31
thinktank wrote:
The average (arithmetic mean) monthly income of four workers is \$2,200. After one worker’s income increases by 25 percent the new average income is \$2,400. What was the original income of the worker whose monthly income increased?

A. \$800
B. \$1,200
C. \$2,400
D. \$3,200
E. It cannot be determined from the information given .

Total salary of 4 workers is 8800

So, a + b + c + d = 8800

Total salary of 4 workers ( after 25% increase in salary of a worker ) is 9600

So, a + a/4 + ( b + c + d ) = 9600

Or, a + a/4 + ( 8800 - a ) = 9600

Or, 4a + a + 35200 - 4a = 38400

Or, a + 35200 = 38400

Or, a = 3200

Hence, correct answer will be (D) 3200

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Re: The average (arithmetic mean) monthly income of four workers   [#permalink] 10 Dec 2016, 11:31
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