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# Over the next ten years, the sales department of a company plans to in

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Math Expert
Joined: 02 Sep 2009
Posts: 44655
Over the next ten years, the sales department of a company plans to in [#permalink]

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25 Dec 2017, 00:48
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Over the next ten years, the sales department of a company plans to increase its staff by 20 percent while the human resources department plans to decrease its staff by 10 percent. If there are currently two hundred total employees between the two departments, and three times as many people work in the sales department as work in the human resources department, how many people will there be in both departments in ten years?

A. 235
B. 225
C. 210
D. 205
E. 200
[Reveal] Spoiler: OA

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Joined: 18 Feb 2017
Posts: 3
Re: Over the next ten years, the sales department of a company plans to in [#permalink]

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25 Dec 2017, 06:16
As per the question stem s+h=200 and s=3h. Solving for s and h gives s=150 and h=50
Now, s' = s in 10 years = 150 + 0.2*150 = 150+30=180 and h' = h in 10 years = 50-0.1*50 = 50-5=45
Therefore, s'+h' =180+45=225. Hence, the correct answer is B.
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Joined: 22 May 2016
Posts: 1569
Over the next ten years, the sales department of a company plans to in [#permalink]

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25 Dec 2017, 11:35
Bunuel wrote:
Over the next ten years, the sales department of a company plans to increase its staff by 20 percent while the human resources department plans to decrease its staff by 10 percent. If there are currently two hundred total employees between the two departments, and three times as many people work in the sales department as work in the human resources department, how many people will there be in both departments in ten years?

A. 235
B. 225
C. 210
D. 205
E. 200

Employees now
There are 200 total employees. There are three times as many in sales as in HR, which is sometimes hard to translate.

For every one HR worker, there are three salespeople: $$\frac{HR}{S} = \frac{1}{3}$$
S = 3HR

HR + S = 200
HR + 3HR = 200, 4HR = 200 ->
HR = 50
S = 3HR = 150

Sales will INcrease by 20 percent
(1 + .20) = 1.2
1.2 * 150 = 180

HR will DEcrease by 10 percent
(1 - 0.10) = .90
.90 * 50 = 45

(180 + 45) = 225 people in 10 years

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Joined: 24 Nov 2016
Posts: 148
Re: Over the next ten years, the sales department of a company plans to in [#permalink]

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25 Dec 2017, 18:50
Bunuel wrote:
Over the next ten years, the sales department of a company plans to increase its staff by 20 percent while the human resources department plans to decrease its staff by 10 percent. If there are currently two hundred total employees between the two departments, and three times as many people work in the sales department as work in the human resources department, how many people will there be in both departments in ten years?

A. 235
B. 225
C. 210
D. 205
E. 200

Sales is S and Human Resources is H: $$S = 3H$$ and $$200=S+H$$, which is $$200=3H+H=4H$$, so $$H=50$$ and $$S=150$$.

After 10 years: $$S = 1.20*S=1.20*150=180$$ and $$H = 0.9*H=0.9*50=45$$.

Total after 10 years in both departments is $$180+45=225$$.

Re: Over the next ten years, the sales department of a company plans to in   [#permalink] 25 Dec 2017, 18:50
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