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.
​

Answer 1

Given :-

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

• 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.

To Find :-

• Number of students in A & B room

Solution :-

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

According to the question,

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

=> x - 10 = y + 10

=> x - y = 20 eq(1)

Again

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

=> 2(y - 20) = x + 20

=> 2y - 40 = x + 20

=> x - 2y = -60 eq (2)

Subtracting (1) from (2), we have

=> x - 2y - (x - y) = -60 - 20

=> x - 2y - x + y = -80

=> -y = -80

=> y = 80

Putting y = 80 in (1), we get

=> x - 80 = 20

=> x = 100

Hence, Number of students in:

1. Room A = 100
2. Room B = 80

____________________

Answer 2

Step-by-step explanation:

Let the number of students in classroom A be x Let the number of students in classroom B be y. If 10 students are transferred from A to B, then we have: x – 10 = y + 10 ⇒x – y = 20 …..(i) If 20 students are transferred from B to A, then we have: 2(y – 20) = x + 20 ⇒2y – 40 = x + 20 ⇒ -x + 2y = 60 …..(ii) On adding (i) and (ii), we get: y = (20 + 60) = 80 On substituting y = 80 in (i), we get: x – 80 = 20 ⇒x = (20 + 80) = 100 Hence, the number of students in classroom A is 100 and the number of students in classroom B is 80. Read more on Sarthaks.com - https://www.sarthaks.com/132577/there-are-classrooms-and-students-are-sent-from-the-number-students-each-room-becomes-same