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In 1990, twice as many boys as girls at Adams High School ea

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In 1990, twice as many boys as girls at Adams High School ea [#permalink] New post   24 Jan 2019, 06:22
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In 1990, twice as many boys as girls at Adams High School earned varsity letters. From 1990 to 2000 the number of girls earning varsity letters increased by 25% while the number of boys earning varsity letters decreased by 25%. What was the ratio in 2000 of the number of girls to the number of boys who earned varsity letters?

A. 53

B. 65

C. 1

D. 56

E. 35
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Re: In 1990, twice as many boys as girls at Adams High School ea [#permalink] New post   25 Jan 2019, 19:40
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Let the number of girls who earned varsity letters be x
then the number of boys who earned varsity letters will be 2x

Now, the number of girls who earned varsity letters increased by 25 in 1 decade.
Therefore, the number of girls at the end of 2000 is 1.25x
In the same time number of boys decreased by 25 therefore their population will be 0.75∗2x=1.5x

Hence, the ratio is 125150=56
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Re: In 1990, twice as many boys as girls at Adams High School ea [#permalink] New post   30 Dec 2024, 19:12
In 1990

Twice as many boys as girls at Adams High School earned varsity letters.
=> B1990=2∗G1990

In 2000

From 1990 to 2000 the number of girls earning varsity letters increased by 25%
=> G2000=G1990+0.25∗G1990=1.25∗G1990

While the number of boys earning varsity letters decreased by 25%.
=> B2000=B1990−0.25∗B1990=0.75∗B1990=0.75∗2∗G1990=1.50∗G1990

What was the ratio in 2000 of the number of girls to the number of boys who earned varsity letters?
=> G2000B2000 = 1.25∗G19901.50∗G1990 = 125150 = 56

So, Answer will be D
Hope it helps!
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Re: In 1990, twice as many boys as girls at Adams High School ea [#permalink]
30 Dec 2024, 19:12
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