The ratio of the number of students in Class A to Class B is 4:5. If 8 students are transferred from B to A, the ratio becomes 5:6. Find the original number of students in each class.

Correct option is A

Given:
Initial ratio of students in Class A to Class B = 4:5
After transferring 8 students from B to A, the new ratio = 5:6
Solution:
Let the original number of students in Class A be 4x and in Class B be 5x.
When 8 students are transferred from B to A, the number of students in A becomes 4x + 8 and in B becomes 5x - 8.
According to the question, the new ratio is 5:6.
​$$\frac{4x + 8}{5x - 8} = \frac{5}{6}$$​​
6 × (4x + 8) = 5 × (5x - 8)
24x + 48 = 25x - 40
25x - 24x = 48 + 40
x = 88
Now, calculate the original number of students.
Original students in A = 4x = 4 × 88 = 352
Original students in B = 5x = 5 × 88 = 440
Final Answer
So the correct answer is (a)