There are 50 students in a hostel. Now the number of students got increased by 8. Due to this the expenses of the mess increased by 30 rupees per day while the average expenditure is decreased by 2 rupees. Find the original expenditure.a)812.5 rupeesb)912.5 rupeesc)1012.5 rupeesd)1112.5 rupeese)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:

Let the original expenditure be x rupees.

Given that the number of students got increased by 8.

So, the total number of students = 50 + 8 = 58.

Also given that the expenses of the mess increased by 30 rupees per day.

So, the new expenditure = (x + 30) rupees.

Given that the average expenditure is decreased by 2 rupees.

Let the original average expenditure be y rupees.

So, y = x/50.

Now, the new average expenditure = (x + 30)/58.

Given that the new average expenditure is decreased by 2 rupees.

So, (x + 30)/58 = y - 2.

Substituting y = x/50 in the above equation, we get

(x + 30)/58 = x/50 - 2

Solving the above equation, we get x = 912.5 rupees.

Therefore, the original expenditure is 912.5 rupees.

Hence, the correct option is (B) 912.5 rupees.

Answer

Answer – b) 912.5 rupees Explanation : Let initial expenditure is E per day. Now it is increased by 30 rupees per day, Initial students = 50 and now they are 58, E/50 – (E + 30)/58 = 2
Solve for E, We will get E = 912.5 rupee.

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