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Question

School A has 30% more student than school B. if 120 more students join school B , The two schools will have the same number of students. what is the sum of the number of students in school A and school B initially ?

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Solution

Let school A and B has x, and y number of students respectively.
Now,
According to the question,
1st condition: x=30% of y+y
x=30100y+y
x=3y10+y
x=3y+10y10
10x=13y
x=13y10 ……..(1)
2nd condition:
y+120=x
x=y+120
13y10=y+120 putting (1)
13y10y=120
13y10y10=120
3y=1200
y=400
x=13×40010=520
Number of student in A school=520
Number of students in B school=400.

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