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Initially, the ratio of potbellied pigs to carrots in a room [#permalink]

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01 May 2013, 09:01

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Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

Re: Initially, the ratio of potbellied pigs to carrots in [#permalink]

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01 May 2013, 09:09

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Aristocrat wrote:

Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A)350 B)300 C)358 D)200 E)275 Can some one explain me with above question

Initially, the ratio of potbellied pigs (P) to carrots (C) in a room had been 1:60. Therefore, \(\frac{P}{C} = \frac{1}{60}\) And there were 6 potbellied pigs in the room, so, \(\frac{P}{C} =\frac{6}{360}\) i.e no. of pigs = 6, no. of carrots initially = 360

After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. Therefore, \(\frac{P}{C} = \frac{3}{1}\) As the number of pigs will remain 6, the no. of pigs and carrots will be \(\frac{P}{C}= \frac{6}{2}\) i.e no. of pigs = 6, no. of carrots remaining = 2

So, Initially there were 360 carrots, and after the pigs ate most of the carrots 2 were left So the pigs ate 360-2 = 358 carrots

Answer : C
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Re: Initially, the ratio of potbellied pigs to carrots in [#permalink]

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01 May 2013, 10:02

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Before \(\frac{P}{C}=\frac{1}{60}\), after \(\frac{P}{C}=\frac{3}{1}\). The only number that changed is C, P is constant and equals 6.

\(\frac{6}{C}=\frac{1}{60}\) means \(C=360\), after \(\frac{6}{C}=\frac{3}{1}\) means there are \(C=2\) left. Number eaten \(360-2=358\) C _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Initially, the ratio of potbellied pigs to carrots in [#permalink]

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01 May 2013, 10:31

Aristocrat wrote:

Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A)350 B)300 C)358 D)200 E)275 Can some one explain me with above question

Given, Ratio Of Potbellied Pigs to Carrots in the room was 1:60 . \(\Rightarrow\) \(\frac{P}{C}=\frac{1}{60}\) . And as Given, Potbellied Pigs was 6 in number, so from this, we have....the following :: \(\frac{P}{C}=\frac{1}{60}\) \(\Rightarrow\) \(\frac{6}{C}=\frac{1}{60}\)

Therefore, C = 360. Now, As Given, Potbellied Pigs ate some number of carrots lets say "x" carrots & the ratio will become 3:1. Therefore, \(\frac{P}{C-x}=\frac{3}{1}\) \(\Rightarrow\) \(\frac{6}{C-x}=\frac{3}{1}\) Therefore, 2 = C- x , or x = C -2 & as we know C = 360. Therefore, X = 360 - 2. Hence, 358.
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Last edited by manishuol on 01 May 2013, 10:55, edited 2 times in total.

Re: Initially, the ratio of potbellied pigs to carrots in [#permalink]

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01 May 2013, 10:52

Aristocrat wrote:

Initially, the ratio of potbellied pigs to carrots in a room had been 1:60. After the potbellied pigs ate most of the carrots, though, the new ratio was 3:1. If there were 6 potbellied pigs in the room, how many carrots did they eat, total?

A)350 B)300 C)358 D)200 E)275 Can some one explain me with above question

The number of pigs remains constant. Initial given ratio : 1:60 = 6:360. Thus there were 360 carrots. Also, as the new ratio is 3:1=[6:the no of carrots left) . Only option C satisfies--> 6:(360-358) = 6:2 = 3:1.
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Re: Initially, the ratio of potbellied pigs to carrots in a room [#permalink]

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25 Dec 2014, 12:30

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