Question

There were 40 students in a hostel. If the number of
students increases by 8, the expenses of the mess
increase by Rs. 48 per day while the average
expenditure per head diminishes by Rs 2. Find the
original expenditure of the mess.
(a) Rs. 700 (b) Rs. 710 (c) Rs. 680 (d) Rs. 720​

Answer 1

Step-by-step explanation:

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Answer 2

The original expenditure of the mess is (d) Rs. 720.

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

To Find: The original expenditure of the mess.

Solution:

Let the expenditure of each student per day be 'x'.

The number of students originally = 40

So, the expenditure of 40 students per day = 40x

It is said that, if the number of students increases by 8, the expenses of the mess increase by Rs. 48 per day while the average expenditure per head diminishes by Rs 2. So, we can say that;

The new total expenditure of 48 students is = 40x + 48

The new expenditure of each student per day = x - 2

So, we can frame an equation with the help of the above conditions;

           ( 40x + 48 ) / 48 = x - 2

       ⇒ 40x + 48 = 48x - 96

       ⇒ 48x - 40x = 144

       ⇒  8x = 144

       ⇒  x = 18

Hence, the expenditure of each student originally is = Rs. 18

So, the original expenditure per day = 40x = Rs. ( 40 × 18 )

                                                             = Rs. 720

Hence, the original expenditure of the mess is (d) Rs. 720.

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