Question

There were 50 students in a hostel. If the number of students increases by 10, then the total expenses for the students increase by Rs. 80 per day while the average expenditure per student diminishes by Rs. 5. Find the total expenditure of all 50 students. 
1. Rs. 1800
2. Rs. 1700
3. Rs. 1950
4. Rs. 1900

Answer 1

Correct Answer - Option 4 : Rs. 1900

Given:

By increasing 10 students, total expenditure increased by Rs.80 

By increasing 10 students, average decreased by Rs.5

Formula Used:

Average = Total expenditure/Number of students

Calculation:

Let the initial average be x

The total expenditure of 50 students = 50 × x = 50x

The total expenditure of 60 students = 50x + 80

The new average = x - 5

According to the question;

⇒ (50x + 80)/60 = (x - 5)

⇒ 50x + 80 = 60x - 300

⇒ 380 = 10x

⇒ x = 38

The total expenditure of 50 students = 50 × 38 = Rs.1900

∴ The total expenditure of 50 students is Rs.1900