Question

When 5 students are shifted from room A to room B, the resulting number of students in the two rooms becomes equal. However if the 5 students are shifted in opposite direction, the resulting students in room A becomes double of those in room B. What is the starting student number in each room?

Answer 1

Solution:

If x & y are starting student numbers in room A and room B respectively. Then from question:

   x - 5 = y + 5

⇒ x - y = 10 - Eq. I

Also from question:

x + 5 = 2 (y - 5)

⇒ x - 2y = -15 - Eq. II

Subtracting Eq. II from Eq. I:

y = 25

Substitute  y = 25 in Eq. I:

x - 25 = 10

⇒ x = 10 + 25 = 35

Thus,

number of students in room A = 35, and

number of students in room B = 25.

From given conditions, number of students in room A = 35, and number of students in room B = 25.