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The ratio of programmers to scientists at a company was 8:5 in the yea

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Bunuel
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The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink] New post   20 Apr 2021, 08:00
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The ratio of programmers to scientists at a company was 8:5 in the year 2000 and 3:4 in the year 2010. If the total number of programmers and scientists at the company was 52 in the year 2000 and 196 in the year 2010, how many more scientists were at the company in 2010 than in 2000?

A. 80
B. 84
C. 88
D. 92
E. 100
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D
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Re: The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink] New post   20 Apr 2021, 08:46
Bunuel wrote:
The ratio of programmers to scientists at a company was 8:5 in the year 2000 and 3:4 in the year 2010. If the total number of programmers and scientists at the company was 52 in the year 2000 and 196 in the year 2010, how many more scientists were at the company in 2010 than in 2000?

A. 80
B. 84
C. 88
D. 92
E. 100


For the year 2000:
Let the number of Programmers be 8x
Scientists = 5x
Given: 13x = 52
x = 4
So, prog. = 32
scientists = 20
For the year 2010:
Let the programmers be 3x
scientists = 4x
7x = 196
x = 28
programmers = 84
scientists = 112
Number of more scientists = 112 - 20 = 92
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Re: The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink] New post   20 Apr 2021, 09:00
Scientists in 2000 = (5/13)(52) = 20
Scientists in 2010 = (4/7)(196) = 112

In the question they were asking how many more scientists in 2010 than 2000 = 112-20 = 92

Ans: Option D
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Re: The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink] New post   16 May 2021, 08:06
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Bunuel wrote:
The ratio of programmers to scientists at a company was 8:5 in the year 2000 and 3:4 in the year 2010. If the total number of programmers and scientists at the company was 52 in the year 2000 and 196 in the year 2010, how many more scientists were at the company in 2010 than in 2000?

A. 80
B. 84
C. 88
D. 92
E. 100

Solution:

We can create an equation for the year 2000 as follows:

8x + 5x = 52

13x = 52

x = 4

So there were 5(4) = 20 scientists at the company in 2000.

Similarly, we can create an equation for year 2010, as follows:

3y + 4y = 196

7y = 196

y = 28

So there were 4(28) = 112 scientists at the company in 2010.

Therefore, there were 112 - 20 = 92 more scientists at the company in 2010 than in 2000.

Answer: D
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Re: The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink] New post   17 May 2021, 02:02
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Year 2000: Total = 52 and Ratio of P : S = 8 : 5 [Total part = 13: \(\frac{52}{13} = 4\)]

=> P = 8 * 4 = 32 and S = 5 * 4 = 20

Year 2010: Total = 196 and Ratio of P : S = 3 : 4 [Total part = 7: \(\frac{196}{7} = 28\)]

=> P = 3 * 28 = 84 and S = 4 * 28 = 112

Scientists 2010 - Scientists 2000= 112 - 20 = 92

Answer D
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Re: The ratio of programmers to scientists at a company was 8:5 in the yea [#permalink]
17 May 2021, 02:02
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