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At a particular company, the average income of managers is $50,000

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At a particular company, the average income of managers is $50,000  [#permalink]

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New post 08 Nov 2018, 03:33
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A
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D
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At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?
A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4

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Re: At a particular company, the average income of managers is $50,000  [#permalink]

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New post 08 Nov 2018, 03:43
2
M/ S = (Difference of sales person from all avg)/ (Difference of managers from all )
=25000/50000
1:2
Answer: D

For above here is formula:
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At a particular company, the average income of managers is $50,000  [#permalink]

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New post 12 Nov 2018, 06:05
Abhi077 wrote:
At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?
A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4



Dear GMATGuruNY

Can you share your thoughts in solving such problem?

Thanks in advance
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Re: At a particular company, the average income of managers is $50,000  [#permalink]

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New post 12 Nov 2018, 06:48
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1
Mo2men wrote:
Abhi077 wrote:
At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?
A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4



Dear GMATGuruNY

Can you share your thoughts in solving such problem?

Thanks in advance


Let the average salary of all the employees = 50,000, implying that the average salary of the managers = 50,000 + 50,000 = 100,000 and that the average salary of the salespeople = 50,000 - 25,000 = 25,000.
To determine the ratio of managers to salespeople, use alligation.

Step 1: Draw a number line, with the averages for the managers and salespeople on the ends and the average for all the employees in the middle:
M 100,000-------------------50,000------------------25,000 S

Step 2: Calculate the distances between the averages.
M 100,000-----50,000-----50,000-----25,000-----25,000 S

Step 3: Determine the ratio in the mixture.
The ratio of M to S is equal to the RECIPROCAL of the distances in red.
M:S = 25000:50000 = 1:2


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Re: At a particular company, the average income of managers is $50,000  [#permalink]

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New post 19 Jun 2019, 06:02
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1
Abhi077 wrote:
At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?
A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4


Easiest way to take this on is consider the average to be any value, let's take $100,000, for the ease of calculation, now we have the average income of managers = $150,000, and the average income of salespeople to be $75,000

Let the number of managers and salespeople be M and S respectively

Now we have, total sum of the income of managers to be 150000*M and total sum of the income of salespeople to be 75000*S

Simply putting in the formula for average, average of all employees = $100,000 = Total Sum of All Employees / Total No. of Employees

(150000*M + 75000*S) divided by (M + S)

$100,000 = (150000*M + 75000*S) divided by (M + S)

Multiplying both sides by (M+S), we get $100,000*(M+S) = 150000*M + 75000*S

Solving this, we get 25000*S = 50000 * M

And solving further, we get M/S = 1/2 (D)

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Re: At a particular company, the average income of managers is $50,000  [#permalink]

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New post 21 Jun 2019, 10:54
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Abhi077 wrote:
At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?
A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4


We can let n = the average income of all employees, s = the number of salespeople and m = the number of managers, and create the following equation (we assume there are no employees other than managers and salespeople):

n = [m(50,000 + n) + s(n - 25,000)]/(m + s)

mn + ns = 50,000m + mn + sn - 25,000s

25,000s = 50,000m

25,000/50,000 = m/s

1/2 = m/s

Answer: D
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Re: At a particular company, the average income of managers is $50,000   [#permalink] 21 Jun 2019, 10:54

At a particular company, the average income of managers is $50,000

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