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The girl:boy ratio in class A was 1:3 and the same ratio in Class B

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The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 13 Oct 2017, 21:42
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Question Stats:

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The girl:boy ratio in class A was 1:3 and the same ratio in Class B was 2:1. When the two classes were combined, the ratio became 1:1. If class A had 24 girls, how many students did class B have?

A) 48
B) 72
C) 96
D) 120
E) 144
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 14 Oct 2017, 02:33
Weighted average question. !!!

For class A :
girls : x
boys : 3x

For class B :
girls : 2y
boys : y
total students : 3y

Now since the ration is 1:1
total number of boys = total number of girls
3x + y = x + 2y
therefore y = 2x

Now, since x = 24
y = 48
and
3y = 144
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 14 Oct 2017, 05:52
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saba4010 wrote:
The girl:boy ratio in class A was 1:3 and the same ratio in Class B was 2:1. When the two classes were combined, the ratio became 1:1. If class A had 24 girls, how many students did class B have?

A) 48
B) 72
C) 96
D) 120
E) 144


No of girls in class \(A =24\)

therefore, no of boys in class \(A = 3*24=72\) (from this we can easily eliminate option A, B & C)

let number of girls in class \(B\) be \(2x\) and no of boys be \(x\). So total students in class \(B =3x\)

When Class \(A\) and \(B\) are mixed its given no boys=no of girls

or \(24+2x=72+x => x=48\)

Hence \(3x= 3*48=144\)

Option E
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 14 Oct 2017, 06:01
Class A => Ratio G:B = 1:3
Where G is number of girls and B is number of boys.
Given G=24 for class A.
B=24x3=72.
In class B, G:B = 2:1
When combining both classes, ratio = 1:1
Therefore, 24+G:72+B=1:1
Solving we get, 24+G=72+B
G=48+B-------(1)
From ratio of class B, we get G=2B-----(2)
Solving equations (1) and (2)
B = 48 and G=96
Total students in class B= 48+96=144
Answer E.

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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 14 Oct 2017, 06:10
Class A

G:B = 1:3. Class A had 24 girls, thus Class A has 24*3 = 72 boys.

Class B

G:B = 2:1. Let the number of boys in class B be x. Thus, the number of girls in Class B is 2x.

It's mentioned that on combining class A and B, the ratio became 1:1 (boys became equal to girls, effectively)

Thus, total number of boys (A and B) = total number of girls (A and B)

--> (72+x)=(24+2x)

--> x = 48.

There are a total of (x+2x = 3x) students in the combined class.

Thus, total number of students = 3x = 3*48 = 144.
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 14 Oct 2017, 07:09
1
saba4010 wrote:
The girl:boy ratio in class A was 1:3 and the same ratio in Class B was 2:1. When the two classes were combined, the ratio became 1:1. If class A had 24 girls, how many students did class B have?

A) 48
B) 72
C) 96
D) 120
E) 144


Class A : Girl : Boy = 1:3
No. of girls = 24
No. of boys = 24*3 = 72
Total = 24 + 72 = 96

Class B : Girl : Boy = 2:1
Let no. of girls & boys are 2x & x respectively
Total = 2x + x = 3x

Now they are mixed and the ratio is 1:1

So, 24 + 2x = 72 + x
x = 48

Also total no. of students in class B = 3x = 3 * 48 = 144

Answer E
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 30 Jun 2018, 16:07
VeritasPrepKarishma how can we solve this question using the formula from mixtures?

I get this and I don't know where is my error:

24/w= (1/2)-(1/4) / (2/3)-(1/2)

So then w= 36 (# of girls in class B)

And 36 + 36/2= 56 (# of students in class B)
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Re: The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 30 Jun 2018, 16:17
24+2x=72+x
X=48
3x=144
Answer E

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The girl:boy ratio in class A was 1:3 and the same ratio in Class B  [#permalink]

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New post 04 Jul 2018, 19:26
saba4010 wrote:
The girl:boy ratio in class A was 1:3 and the same ratio in Class B was 2:1. When the two classes were combined, the ratio became 1:1. If class A had 24 girls, how many students did class B have?

A) 48
B) 72
C) 96
D) 120
E) 144


Since class A has 24 girls, there are 24 x 3 = 72 boys in the class.

We also know that in class B, the ratio of girls : boys = 2x : x

The new combined ratio of 1:1 can be expressed as 1/1, or 1. We can thus create the equation:

(24 + 2x)/(72 + x) = 1

24 + 2x = 72 + x

x = 48

Class B had x = 48 boys and 2x = 96 girls, so class B had 48 + 96 = 144 total students.

Answer: E
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