In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?

Question: In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?

Solution:
Let, the average expenditure of initial students be x,

ATQ,
52x + 510 = (52 + 18) × (x - 3)
⇒ 52x + 510 = 70x - 210
⇒ 70x - 52x = 510 + 210
⇒ 18x = 720
∴ x = 40

Hence, the total expenditure of 52 students = 52 × 40 = 2080 tk.