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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Last year, the ratio of nonfiction to fiction books in a home library  [#permalink]

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20 Mar 2018, 22:17
00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:30) correct 15% (02:45) wrong based on 54 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

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

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20 Mar 2018, 23:24
1
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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Posts: 188
Re: Last year, the ratio of nonfiction to fiction books in a home library  [#permalink]

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25 Mar 2018, 02:50
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, 02:50
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