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# Class B has 50% more students than class A. Number of girls in class A

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Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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07 Jun 2017, 04:05
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Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %

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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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07 Jun 2017, 04:22
Since class B has 50% more students, if class A has 100 students, class B has 150 students.

If percentage of girls is same in both the classes and girls in class A is same as boys in class B, the number of girls must be 60(60%) because 60% in class B is 90 in class B. This makes the number of boys in class B(60)

Total number of boys is 40(class A) + 60(class B)/Total students:250 = 40%(Option C)
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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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07 Jun 2017, 07:22
Top Contributor
understandZERO wrote:
Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %

Class B has 50% more students than class A.
Let's choose some nice values that work with this information. How about:
TOTAL number of students in class A = 100
TOTAL number of students in class B = 150

Number of girls in class A is equal to number of boys in class B.
Let x = number of girls in class A
So, x = number of boys in class B

This ALSO means that 100-x = number of boys in class B
And 150-x = number of girls in class B

The percentage of girls is the same in both classes.
In other words, the proportion of girls is the same in both classes.
In class A, the proportion of girls to the TOTAL class A population = x/100
In class B, the proportion of girls to the TOTAL class B population = (150-x)/150
So, we can write: x/100 = (150-x)/150
Cross multiply: 150x = 100(150-x)
Simplify: 150x = 15000 - 200x
Add 200 x to both sides: 250x = 15000
Solve: x = 60

So, there are 60 girls in class A and 60 boys in class B
We can also conclude that there are 40 boys in class A

What percentage of the student group are boys?
Total number of boys = 60 + 40 = 100
Total population = 100 + 150 = 250

So the PROPORTION of boys = 100/250 = 2/5
2/5 = 40%

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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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08 Jun 2017, 04:20
Let Ga = No. of Girls in class A
Ba = No. of Boys in class A
Gb= No. of Girls in class B
Bb= No. of Boys in class B

Given:
Ga= Bb
and (Ga+Ba)1.5 = Gb+Bb

To find: (Ba+Bb) / (Ga+Ba+Gb+Bb)

= (Ba+Bb) /{(2.5) (Ga+Ba)}
= (Ba+Bb) /{(2.5) (Bb+Ba)}
= 1/ 2.5

In % = 2/5*100 = 40%

Hence ans C
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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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10 Jun 2017, 07:30
understandZERO wrote:
Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %

Let the number of students in class A be 2x. Since the number of students in class B is 50% more, it is (1.5)2x = 3x.

Denote the number of boys in class B by y. Since the number of girls in class A is the same as the number of boys in class B, it is also y. Since there are 2x students in class A and y of them are girls, there are 2x - y boys in class A. Thus, in class A and B, there are (2x - y) + y = 2x boys. Therefore, the percentage of boys in the two classes combined is 2x/5x = 2/5 = 40%.

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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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10 Jun 2017, 10:05
Let the total student in A = 100, so B = 150.
Now Ga = Girls in A and Ba Boys in A
Similarly Gb = Girls in B and Bb boys in B

Now Class A: 100 = Ga+Ba
Class B : 150 = Gb + Bb
Since given Ga = Bb we get
100 = Ba + Bb - So the total boys are 100. Total students are 250.
So Boys % = (Total Boys/ Total Students)*100
Boys % = 100/250 * 100 = 40%
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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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10 Jun 2017, 11:34
This was an easy one. I tried it out with an X approach. and it worked out straight.

Assume Students in Class A : 2X, Students in class B : 3X, Girls in Class A = Boys in Class B: Y, Girls in Class B = 3X-Y, Boys on class A : 2X-y

So total boys are : 2X, total student : 5X, so % is 40
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Re: Class B has 50% more students than class A. Number of girls in class A  [#permalink]

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09 Apr 2018, 08:37
let, the total students are in class A is 1 and total girl is X, so boys will be (1-x) in class A.
let, the total students are in class B is 3/2= 1.5 and total girl is Y, so boys will be (3/2- Y) in class B.
according to the question,
X = 3/2 - Y
> X + Y = 3/2
hence, total students are (1 + 3/2) = 5/2, and girls no is 3/2
so, boys will be (5/2 - 3/2)= 1
Then, 1/(5/2) *100% = 40% are boys
Re: Class B has 50% more students than class A. Number of girls in class A &nbs [#permalink] 09 Apr 2018, 08:37
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