Question

. A part of monthly charges in a hostel are fixed and remaining depend on the number

of days one taken food in the mess. When a student X takes food for 25days, he has to pay

Rs. 1750 as hostel charges, whereas a student Y who takes food for 28 days , pays Rs. 1900 as

hostel charges. Find the fixed charges and the cost of food per day.

please answer​

Answer 1

Answer:

Fixed charge = Rs. 500

Cost per day = Rs. 50

Step-by-step explanation:

Let the fixed charge be Rs. x

Let the cost per day be Rs. y

Case 1 - Student X takes food for 25 days and he has to pay  Rs. 1750 as hostel charges

Fixed charge = Rs. x

Cost per 1 day = Rs. y

=> Cost per 25 days = y * 25 = Rs. 25y

So total cost = Fixed charge + Charge based on number of days

=> Total cost = x + 25y

But the total cost = Rs. 1750 (given)

=> x + 25y = 1750 ------------------> EQUATION 1

Case 2 - Student Y takes food for 28 days and pays Rs. 1900 as  hostel charges

Fixed charge = Rs. x

Cost per 1 day = Rs. y

=> Cost per 28 days = 28y

So total cost = Fixed charge + Charge based on number of days

=> Total cost = x + 28y

But the total cost = Rs. 1900

=> x + 28y = 1900 ------------------> EQUATION 2

Subtract EQUATION 2 - EQUATION 1

=>   ( x + 28y = 1900 )

   -  ( x + 25y = 1750 )

====================

       0x + 3y = 150

====================

=> 3y = 150

=> y = 150 / 3

= 50

Apply y = 50 in EQUATION 1

x + 25y = 1750

=> x + 25(50) = 1750

=> x + 1250 = 1750

=> x = 1750 - 1250

= 500

So x = 500

     y =  50

Therefore the fixed charge is Rs. 500 and the cost per day is Rs. 50