The average (arithmetic mean) monthly income of four workers

Question

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 .

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

mau5 · Accepted Answer

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.

LalaB · Answer

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

Bunuel · Answer

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.

Answer: D.

Hope it's clear.

MarkHanna · Answer

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!

ENGRTOMBA2018 · Answer

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$.

MarkHanna · Answer

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

Thanks!

stonecold · Answer

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
Added su => 200*4=> 800
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

Abhishek009 · Answer

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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The average (arithmetic mean) monthly income of four workers

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The average (arithmetic mean) monthly income of four workers

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