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A hostel has 50 students. If the number of students is increased by 10, the maintenance cost increases by Rs. 40/day, while the average maintenance cost per person decreases by Rs. 4. What is the basic maintenance cost of the hostel per day?

A hostel has 50 students. If the number of students is increased by 10, the maintenance cost increases by Rs. 40/day, while the average maintenance cost per person decreases by Rs. 4. What is the basic maintenance cost of the hostel per day? Correct Answer Rs. 1400 

Given:

If the number of students is increased by 10, then

The maintenance cost increases = Rs. 40/day

The average maintenance cost per person decreases = Rs. 4

Formula used:

Average = Sum of observations/Total number of observations

Calculation:

Let the average maintenance cost be x.

According to the question,

50x + 40 = 60(x - 4)

⇒ 50x + 40 = 60x - 240

⇒ 10x = 280

⇒ x = 28

Now, the basic maintenance cost of the hostel per day = 50x

⇒ 50 × 28

⇒ Rs. 1400

∴ The required maintenance cost of the hostel per day is Rs. 1400.

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