There are two examinations rooms A and B. If 10 students are sent from A to B,…
2023
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
- A.
150
- B.
80
- C.
100
- D.
200
Attempted by 150 students.
Show answer & explanation
Correct answer: C
Let the number of students in rooms A and B be x and y respectively.
From sending 10 students from A to B: x - 10 = y + 10, which simplifies to x - y = 20.
From sending 20 students from B to A: x + 20 = 2(y - 20). Expanding gives x + 20 = 2y - 40, so x - 2y = -60.
Solve the two equations: x - y = 20 and x - 2y = -60. Subtract the second from the first or substitute: (x - y) - (x - 2y) = 20 - (-60) ⇒ y = 80.
Then x = y + 20 = 80 + 20 = 100.
Therefore, the number of students in room A is 100.