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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 ........  [#permalink]

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New post 29 Nov 2018, 04:39
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A
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C
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E

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Question Stats:

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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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Re: In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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New post 29 Nov 2018, 06:02
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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.
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Re: In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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New post 03 Dec 2018, 05:11

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 = \(100 * [\frac{(48y – 40y)}{30}]/\frac{40y}{30} = 20\)%

Hence, the correct answer is option C.

Answer: C

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In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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New post 22 Nov 2019, 05:34
EgmatQuantExpert wrote:
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%


\(Average=Sum*n\)

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

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

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

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

Ans (C)
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In a department of 30 employees, the average salary of top 10 ........   [#permalink] 22 Nov 2019, 05:34
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