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Last year, the ratio of nonfiction to fiction books in a home library

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Joined: 02 Sep 2009
Posts: 44635
Last year, the ratio of nonfiction to fiction books in a home library [#permalink]

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New post 20 Mar 2018, 23:17
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  25% (medium)

Question Stats:

89% (01:06) correct 11% (02:45) wrong based on 44 sessions

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Last year, the ratio of nonfiction to fiction books in a home library was 1 to 30. This year, the number of nonfiction books increased by 5 and the number of fiction books increased by 50, making the ratio of nonfiction to fiction books 1 to 25. What was the number of nonfiction books last year?

(A) 15
(B) 12
(C) 10
(D) 8
(E) 5
[Reveal] Spoiler: OA

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Re: Last year, the ratio of nonfiction to fiction books in a home library [#permalink]

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New post 21 Mar 2018, 00:24
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Bunuel wrote:
Last year, the ratio of nonfiction to fiction books in a home library was 1 to 30. This year, the number of nonfiction books increased by 5 and the number of fiction books increased by 50, making the ratio of nonfiction to fiction books 1 to 25. What was the number of nonfiction books last year?

(A) 15
(B) 12
(C) 10
(D) 8
(E) 5


IMO A.

Let the non-fiction books last year be t.
So the fiction books last year would be 30t.

5 books were added to t and 50 books were added to 30t and new ratio was 1 : 25

\((t+5)/(30t+50) = 1/25\)

Solving for t

\(25t + 125 = 30t + 50\)
\(5t = 75\)
\(t = 15\)

Hence A.

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Gladi
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Posts: 105
Re: Last year, the ratio of nonfiction to fiction books in a home library [#permalink]

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New post 25 Mar 2018, 03:50
Initial Ratio: 1/30
Let Common Multiplier for Initial Ratio be: x
We get x/30x

Final Ratio: 1/25

Given: (x+5)/(30x+50) = 1/25

Plugin Ans choices:
x=15, LHS=RHS

Ans A

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Re: Last year, the ratio of nonfiction to fiction books in a home library   [#permalink] 25 Mar 2018, 03:50
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Last year, the ratio of nonfiction to fiction books in a home library

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