Question

Some students are sitting in classroom A and B in a school. When 10 students
from room A are sent to room B, the number of students in both rooms becomes
equal. When 20 students from room B are sent to room A, then the number of
students in room A becomes twice that in room B. Find the number of students
each room.
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Answer 1

Let the number of students in class A and class B be x and y respectively.

According to the question,

Case First :-

When 10 students from room A are sent to room B, the number of students in both rooms becomes.

⇒ Students in Room A - 10 = Students in Room B + 10

⇒ x - 10 = y + 10

⇒ x - y = 20 ...(1)

Case Second :-

When 20 students from room B are sent to room A, then the number of students in room A becomes twice that in room B

⇒ 2(Students in room B - 20) = Students in room A - 20

⇒ 2(y - 20) = x + 20

⇒ 2y - 40 = x + 20

⇒ x - 2y = -60 ...(2)

Subtracting (1) from (2), we have

⇒ x - 2y - (x - y) = -60 - 20

⇒ x - 2y - x + y = -80

⇒ -y = -80

⇒ y = 80

Now, Substituting y = 80 in (1), we get

⇒ x - 80 = 20

⇒ x = 100

Hence, Number of students in:

• Room A = 100
• Room B = 80

Answer 2

Let the number of students in rooms A and B be x and y respectively.

⇒ x - 10 = y + 10      x - y = 20 .... (i)

    and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

Solving (i) and (ii) by substitution method

x - y = 20

-x -(-2y) = 60

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y = 80

Put value of y in equation (i)

⇒ x - 80 = 20

⇒ x = 20 + 80

⇒ x = 100

∴ x = 100 and y = 80.