how to solve that there are two classrooms a and b. if 10 students are shifted from a to b than the number of students  in each room becomes same . if 20 students are send from b to a the number of students  in a becomes double of b . find the students in each room.

a-10 = b+10  --------- 1

a+20 =2 x b  --------2

on solving this we get

2a = 3b -------- 3

Multiply 1 by 2

2a - 20 = 2b +20

2a = 2b +40

sub 2a = 3b here

3b = 2b + 40

3b - 2b = 40

b = 40

sub b = 40 in 2

a + 20 = 2 x b

a + 20= 2 x 40

a + 20 = 80

a = 80-20

a = 60

Therefore number of students in the classroom a is 60 and the classroom b is 40

 Let the number of students in classroom 'a' be 'p'

Let the number of students in classroom 'b' be 'r'

As per question,

p-10=r+10

=>p-r=10+10

=>p-r=20 -----(1)

=> p=20+r-----(2)

Next condition,

p+20=2(r-20) -----(3)

Substituting the value of (2) in (3),

20+r+20=2r-40

=> 40+40= 2r-r

=> 80=r

Now, p= 20+r

=> p=20+80=100

Therefore value of p is 100 and r is 80

Required Answer,

Number of Students in Classroom 'a'=p=100 students.

Number of students in classroom 'b'= r= 80 students.

Answer---> Classroom a'' consists of 100 students while classroom 'b' consists of 80 students