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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3209
In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 59% (02:36) correct 41% (02:54) wrong based on 85 sessions

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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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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1044
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities)
Re: In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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2
1
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%

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3209
Re: In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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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.

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VP  P
Joined: 24 Nov 2016
Posts: 1068
Location: United States
In a department of 30 employees, the average salary of top 10 ........  [#permalink]

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