In a department of 30 employees, the average salary of top 10 ........

Question

In a department of 30 employees, the average salary of top 10 employees was twice the average salary of the remaining employees. If the average salary of top 10 employees is increased by 30% and the average salary of the remaining employees is increased by 10%, then what is the percentage increase in the average salary of all the employees?

A. 10%
B. 15%
C. 20%
D. 25%
E. 40%

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A.  10%
 B.  15%
 C.  20%
 D.  25%
 E.  40%

To read all our articles: Must read articles to reach Q51

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Chethan92 · Accepted Answer

Let the average salary of Top 10 employees be 200. 
Let the average salary of the remaining 20 employees be 100.

Average salary of 30 employees = 200*10+100*20 = 4000/30 = 400/3

The average salary of top 10 employees after 30% increase = 260.
The average salary of the remaining 20employees after 10% increase = 110.

New Average salary of 30 employees = 260*10+110*20 = 4800/30 = 480/3

Percentage increase = (480/3 - 400/3)/400/3 = 80/3*3/400 = 1/5*100 = 20%

C is the answer.

EgmatQuantExpert · Answer

Solution 
  Given:  
 • In a department of people, there are 30 employees
• The average salary of top 10 employees = the average salary of the remaining employees
• Average salary of top 10 employees is increased by 30%
• Average salary of the remaining employees is increased by 10%

To find:  
 • The percentage increase in the average salary of all the employees

Approach and Working:  
 • The average salary of top 10 employees = sum of the salaries of the top 10 employees/10
 o Let this be equal to x

• The average salary of remaining 20 employees = sum of the salaries of the remaining 20 employees/20
 o Let this be equal to y

• From these, we get the sum of salaries of all employees = 10x + 20y
• And we are given that x = 2y
 o Thus, average salary of all employees =  \frac{(10x + 20y)}{30} = \frac{40y}{30}

• The new average salary of top 10 employees = x + 30% of x = 1.3x
• The new average salary of remaining 20 employees = y + 10% of y = 1.1y
• From these equations, we get the new sum of salaries of all employees = 10 * 1.3x + 20 * 1.1y = 13x + 22y
 o Thus, the new average salary of all employees =  \frac{(13x + 22y)}{30} = \frac{48y}{30}

Therefore, the percentage increase in average salary of all employees =  100 *  /\frac{40y}{30} = 20 %

Hence, the correct answer is option C.

Answer: C

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exc4libur · Answer

Average=Sum*n

n=30…avg_{20}=m…avg_{10}=2*avg_{20}=2m

before:avg_{all}=\frac{10*2m+20*m}{30}=4m/3

after:avg_{all}=\frac{10*1.3(2m)+20*1.1(m)}{30}=\frac{26m+22m}{30}=48m/30=8m/5

per.inc:\frac{after}{before}-1…\frac{(8m/5)}{(4m/3)}-1…6/5-1=1/5=0.2

Ans (C)

ScottTargetTestPrep · Answer

Solution:

We can let the top 10 employees’ salaries be $300 each and the remaining 20 employees’ salaries be $150 each. We see that the average salary of all 30 employees is (10 x 300 + 20 x 150)/30 = 6000/30 = $200.

If the salary of the top 10 employees is increased by 30%, then their new salary is 300 x 1.3 = $390. If the salary of the remaining 20 employees is increased by 10%, then their new salary is 150 x 1.1 = $165. Therefore, the new average salary of the 30 employees is (10 x 390 + 20 x 165)/30 = 7200/30 = $240. We see that this is an increase of $40 from the orginal average salary of $200, or an increase of $20 per $100, which is a 20% increase.

Answer: C

Dereno · Answer

Given that the total number of employees = 30.

Average of Top 10 employees = 2 * Average of the remaining employees

If the average of the remaining is a.

Average of Top 10 employees = 2a

Let’s calculate the sum for this case: Average = (sum/ number of elements)

Sum of top 10 employees = Average of top 10 * Number of elements

= 2a * 10

= 20a

Sum of the remaining 20 employees = Average of the remaining 20 employees * Number of elements

= a * 20

= 20a

Total sum of the 30 employees = 20a + 20a = 40a

Percentage increase of averages :

For the Top 10 employees = 1.3 * (2a) = 2.6a

For the remaining 20 employees = 1.1 * a = 1.1a

Sum of the top 10 employees = (2.6a *10) = 26a

Sum of the remaining 20 employees = 20* (1.1a) = 22a

Total new sum = 26a + 22a = 48a

Since, average = sum / n , where n remains the same in both cases. We find the sum percent increase

% increase = (48a - 40a) / (40a)

= 8a/40a

= (1/5)*100

= 20%

Option C

In a department of 30 employees, the average salary of top 10 ........

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In a department of 30 employees, the average salary of top 10 ........

Prep Toolkit

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