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There were 40 students in a hostel. If the number increases by 8,the expenses of the mess increase by 48 per day while the average expenditure per head diminishes by 2. Find the original expenditure of the mess.?
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There were 40 students in a hostel. If the number increases by 8,the e...
Solution:

Let's assume that the original expense per day of the mess was x.

Given, there were 40 students in the hostel.

After the increase of 8 students, the total number of students in the hostel becomes 40+8=48.

The new expense per day of the mess after the increase in the number of students is x+48.

The average expenditure per head after the increase in the number of students is (x+48)/48.

It is given that the average expenditure per head diminishes by 2.

So, the new average expenditure per head will be (x+48)/48 - 2.

We can equate this new average expenditure per head with the original average expenditure per head, which was x/40.

(x+48)/48 - 2 = x/40

Multiplying both sides by 48*40, we get:

40(x+48) - 2*48*40 = 48x

Simplifying this equation, we get:

40x + 40*48 - 2*48*40 = 48x

40*48 - 2*48*40 = 8x

Solving for x, we get:

x = (40*48 - 2*48*40)/8

x = 240

Therefore, the original expenditure of the mess was Rs. 240 per day.

Explanation:

- We assumed the original expense per day of the mess as x.
- We used the given information to find the new expense per day of the mess after the increase in the number of students and the new average expenditure per head.
- We equated the new average expenditure per head with the original average expenditure per head and solved for x to find the original expenditure of the mess.
- We got the value of x as 240, which means the original expenditure of the mess was Rs. 240 per day.
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There were 40 students in a hostel. If the number increases by 8,the e...
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There were 40 students in a hostel. If the number increases by 8,the expenses of the mess increase by 48 per day while the average expenditure per head diminishes by 2. Find the original expenditure of the mess.?
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There were 40 students in a hostel. If the number increases by 8,the expenses of the mess increase by 48 per day while the average expenditure per head diminishes by 2. Find the original expenditure of the mess.? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about There were 40 students in a hostel. If the number increases by 8,the expenses of the mess increase by 48 per day while the average expenditure per head diminishes by 2. Find the original expenditure of the mess.? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There were 40 students in a hostel. If the number increases by 8,the expenses of the mess increase by 48 per day while the average expenditure per head diminishes by 2. Find the original expenditure of the mess.?.
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