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

Question

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

ApplicantX · Accepted Answer

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

niks18 · Answer

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

souvonik2k · Answer

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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Heisenberg12 · Answer

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.

shashankism · Answer

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

dimmak · Answer

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)

gmatzpractice · Answer

24+2x=72+x
X=48
3x=144
Answer E

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ScottTargetTestPrep · Answer

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

QuantMadeEasy · Answer

Class A 
boys - 72
girls - 24

Class B 
Boys - x
girls - 2x

after combining
72+ x = 24 +2x
x = 48

Class B students 3*48 = 144
E is correct

Kinshook · Answer

Class ********* Boys *************Girls **************Total
A ************* 3k *************** k ****************** 4k
B ************* m **************** 2m **************** 3m
Combined***** 3k + m ********* k + 2m ************* 4k + 3m

3k + m = k + 2m
2k = m

Class ********* Boys *************Girls **************Total
A ************* 3k *************** k =24************** 4k
B ************* 2k **************** 4k **************** 6k
Combined***** 5k ***************** 5k ************* 10k

Number of students in class B = 6k = 6 * 24 = 144

IMO E

MercedesF1 · Answer

KarishmaB   GMATNinja  I tried using the weighted average but getting the answer wrong.

W1/W2 = A2-Avg/Avg-A1

24/W2 = 2/3 - 1/2 / 1/2 - 1/4

W2 = 36 and Total Students in B = 54.

KarishmaB · Answer

What you did is correct but your interpretation of what you have got as the answer is not. We get w1/w2 = 2/3 but what are the weights here? I say 1/4 of the class is girls and 2/3 of the class is girls. Hence my weights w1 and w2 are the 'total number of students in each class' If class A had 24 girls, it had 4*24 = 96 total students. So class B had total 144 students. Answer (E) Check this: https://anaprep.com/arithmetic-weights- ... d-average/

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

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