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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?

The percentage of the whole student group that are boys is 40%.

Step-by-step setup

Let:

  • Students in Class A = NNN
  • Then students in Class B = 1.5N1.5N1.5N (because B has 50% more than A).

Let in Class A:

  • Girls = GAG_AGA​
  • Boys = BAB_ABA​

So:

  • N=GA+BAN=G_A+B_AN=GA​+BA​

Given:

  1. Number of girls in A = number of boys in B

GA=BBG_A=B_BGA​=BB​

  1. Percentage of girls is the same in both classes.

Let that common percentage of girls be p%p%p%.

Expressing each class in terms of ppp

In Class A :

  • Girls GA=p%G_A=p%GA​=p% of N=p100NN=\dfrac{p}{100}NN=100p​N
  • Boys BA=N−GA=N−p100N=(1−p100)NB_A=N-G_A=N-\dfrac{p}{100}N=\left(1-\dfrac{p}{100}\right)NBA​=N−GA​=N−100p​N=(1−100p​)N

In Class B :

  • Total students = 1.5N1.5N1.5N
  • Girls GB=p%G_B=p%GB​=p% of 1.5N=p100⋅1.5N=3p200N1.5N=\dfrac{p}{100}\cdot 1.5N=\dfrac{3p}{200}N1.5N=100p​⋅1.5N=2003p​N
  • Boys BB=1.5N−GB=1.5N−3p200NB_B=1.5N-G_B=1.5N-\dfrac{3p}{200}NBB​=1.5N−GB​=1.5N−2003p​N

Using the key condition

Condition:
Number of girls in A = number of boys in B

GA=BBG_A=B_BGA​=BB​

Substitute:

p100N=1.5N−3p200N\dfrac{p}{100}N=1.5N-\dfrac{3p}{200}N100p​N=1.5N−2003p​N

Divide both sides by NNN (non-zero):

p100=1.5−3p200\dfrac{p}{100}=1.5-\dfrac{3p}{200}100p​=1.5−2003p​

Multiply everything by 200 to clear denominators:

2p=300−3p2p=300-3p2p=300−3p

2p+3p=3002p+3p=3002p+3p=300

5p=300 \Rightarrowp=60

So 60% are girls in each class.

Find percentage of boys in the whole group

If 60% of the whole group are girls, then boys are:

100%-60%=40%

So, 40% of the combined students (A + B) are boys.

Quick numeric check (example)

Take a convenient total for Class A:

  • Let Class A have N=100 students.
    • Girls in A = 60
    • Boys in A = 40

Then Class B has 1.5N=150 students.

  • Girls in B must also be 60% of 150 = 90
  • Boys in B = 150 − 90 = 60

Now check conditions:

  • Girls in A = 60
  • Boys in B = 60 → condition satisfied
  • Girls % in A = 60/100 = 60%
  • Girls % in B = 90/150 = 60%

Total students = 100 + 150 = 250
Total boys = 40 + 60 = 100 Percentage of boys in whole group = 100/250=40%. ✅

Answer: 40% of the student group are boys.