Q8 of 71 Page 68

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. Yash takes food for 25 days. He has to pay Rs. 2200 as hostel charges where as Niyati takes food for 20 days. She has to pay Rs. 1800 as hostel charges. Find the fixed charges and the cost of food per day.

Let the fixed charge be Rs x and the cost of food per day be Rs y.


According to the question,


For Yash,


He took food for 25 days


⇒ x + 25 y = 2200..(i)


For Niyati,


She took food for 20 days


⇒ x + 20 y = 1800….(ii)


Subtract (ii) from (i),


x + 25y – x – 20 y = 2200 – 1800


⇒ 5y = 400


⇒ y = 80


Putting this value in (i),


x + 25× 80 = 2200


⇒ x = 2200 – 2000


⇒ x = 200


Hence, the fixed cost = Rs 200 and the cost for food per day = Rs 80


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