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From a group of boys and girls, 15 girls leave. There are then left tw

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From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 11 Oct 2011, 02:33
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A
B
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Difficulty:

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Question Stats:

74% (02:15) correct 26% (03:38) wrong based on 23 sessions

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From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:

1) 29
2) 40
3) 43
4) 48
5) None of these

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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 11 Oct 2011, 04:08
jamifahad wrote:
From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:
1) 29
2) 40
3) 43
4) 48
5) None of these


Algebraically;
B=2(G-15)
5(B-45)=G-15

PIN:
G=29; G-15=14; B=14*2=28; How can 45 boys leave out of 28.
G=40; G-15=25; B=25*2=50; 50-45=5; 5*5=25. Matches the count of girls.

Ans: "B"
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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 11 Oct 2011, 04:13
lets take Boys in the group = X
girls= Y

After 15 girls leave

2(Y-15) = X ---(1)

After 45 boys leave

(Y-15) = 5(X-45)

Y-15=5X-225

X=(Y+210)/5 ---(2)

(1) and (2) combined
X= 2Y-30 = (Y+210)/5==> 10Y-150 = Y+210

360 = 9Y

Y= 40
Number of girls at the begininig = 40
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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 11 Oct 2011, 05:47
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jamifahad wrote:
From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:
1) 29
2) 40
3) 43
4) 48
5) None of these



Solve it using choices.

take choice 1) 29 girls

15 girls leave .So, only 14 girls left. Given 2 boys are left for each girl so number of boys should be 28.However , next step where 45 boys leave would not satisfy.

Lets try choice 2) 40 girls. 15 girls leave so left is 25 girls. Boys will be 50 then.
Next step ; 45 boys leave so only 5 boys left and 5 girls for each boy.Satisfies

This perfectly fits our conditions.Hence option (2)40 is the answer.
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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 11 Oct 2011, 07:24
Initial # Boys=B #of Girls=G

if 15 girls leave, B/2= (G-15) or, B= 2G-30
if 45 Boys leave, (B-45)= (G-15)/5 or, B= (G-15)/5+45
Therefore, 2G-30= (G-15)/5+45
solving for G: G=40
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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 19 Mar 2018, 06:45
jamifahad wrote:
From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:

1) 29
2) 40
3) 43
4) 48
5) None of these


We can let b = number of boys and g = number of girls originally in the group. Thus, we have:

b/(g - 15) = 2/1

and

(b - 45)/(g - 15) = 1/5

Simplifying the first equation, we have:

b = 2(g - 15)

b = 2g - 30

Substituting this into the second equation, we have:

(2g - 30 - 45)/(g - 15) = 1/5

5(2g - 75) = g - 15

10g - 375 = g - 15

9g = 360

g = 40

Answer: B
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Re: From a group of boys and girls, 15 girls leave. There are then left tw  [#permalink]

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New post 26 Mar 2019, 21:59
jamifahad wrote:
From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:

1) 29
2) 40
3) 43
4) 48
5) None of these


Use a single variable. Say number of girls in the beginning is G.

When 15 leave, we have (G - 15) girls. At this time, we have twice the number of boys i.e. 2*(G - 15)

When 45 boys leave, we have [2*(G - 15) - 45] boys. This number is 1/5th of the number of girls.

2G - 75 = (1/5)*(G - 15)
10G - 375 = G - 15
9G = 360
G = 40

Answer (B)
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Re: From a group of boys and girls, 15 girls leave. There are then left tw   [#permalink] 26 Mar 2019, 21:59
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