Q12 of 186 Page 4

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay Rs. 1000 as hostel charges, whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and cost of food per day.

Let fixed hostel charge (monthly) = Rs x

and cost of food for one day = Rs y


In case of student A,


x + 20y = 1000


x + 20y – 1000 = 0 …(i)


In case of student B,


x + 26y = 1180


x + 26y – 1180 = 0 …(ii)


By cross - multiplication method, we have





On taking I and III ratio, we get



⇒ x = 400


On taking II and III ratio, we get



⇒ y = 30


Hence, monthly fixed charges is Rs. 400 and cost of food per day is Rs. 30


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