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.