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# The current ratio of boys to girls at a certain school is 2 to 5. If 1

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Math Expert
Joined: 02 Sep 2009
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The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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15 Jan 2018, 05:46
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Difficulty:

25% (medium)

Question Stats:

76% (01:32) correct 24% (02:01) wrong based on 87 sessions

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The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school?

(A) 27
(B) 48
(C) 54
(D) 72
(E) 108

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Re: The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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15 Jan 2018, 08:16
Bunuel wrote:
The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school?

(A) 27
(B) 48
(C) 54
(D) 72
(E) 108

B:G = 2:5

let, B = 2a
and G = 5a

after adding 12 Boys, Boys now = 2a+12
Girls now = 5a

New Ratio = 2a+12 / 5a = 4/9

i.e. a+6 / 5a = 2/9

i.e. 9a +54 = 10a
i.e. a = 54

Now, Boys = 2a = 2*54 = 108

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The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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17 Jan 2018, 07:32
(2x+12)/(5x) = (4/9)
2x=108

Ans. E.
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Joined: 31 Dec 2017
Posts: 89
Re: The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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02 Jun 2019, 05:41
I have another approach:
B:G= 2:5
(B+12):G=4:9 --> (B/G) + (12/G) = 4/9
(2/5) + (12/G) = 4/9 -->(2G +60)/5G= (4/9) (I replace B/G by the ratio 2/5)-->G=270
(B/G)= (2/5) (replace G=270)-->B=108

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Re: The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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02 Jun 2019, 08:56
Bunuel wrote:
The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school?

(A) 27
(B) 48
(C) 54
(D) 72
(E) 108

$$\frac{2x + 12}{5x} = \frac{4}{9}$$

Or, $$18x + 108 = 20x$$

Or, $$2x = 108$$

Or, $$x = 54$$

So, The total number of boys is $$2*54 = 108$$ , Answer must be (E)
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Joined: 07 Dec 2014
Posts: 1222
Re: The current ratio of boys to girls at a certain school is 2 to 5. If 1  [#permalink]

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02 Jun 2019, 18:36
Bunuel wrote:
The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school?

(A) 27
(B) 48
(C) 54
(D) 72
(E) 108

b/g=2/5→
4g=10b, equation 1
(b+12)/g=4/9→
4g=9b+108, equation 2
subtracting 2 from 1,
b=108
E
Re: The current ratio of boys to girls at a certain school is 2 to 5. If 1   [#permalink] 02 Jun 2019, 18:36
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