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The remaining portion of the monthly hostel fee at a college dorm is determined by how many days the resident has consumed meals from the mess. When a student A takes food for 25 days, he has to pay ₹ 4,500, whereas a student B who takes food for 30 days, has to pay ₹ 5,200. What are the monthly fixed costs and the daily food costs, respectively?

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Fixed charge per month is ₹140 and the cost of food per day is ₹1000

Fixed charge per month is ₹450 and the cost of food per day is ₹35

Fixed charge per month is ₹350 and the cost of food per day is ₹25

Fixed charge per month is ₹1,000 and the cost of food per day is ₹140

answer is C.

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Detailed Solution

It is given that student A takes food for 25 days of ₹4,500 and student B takes food for 30 days of ₹ 5,200.
Let the fixed monthly hostel charges be ₹ x and the cost of food per day taken from the mess be ₹ y.
According to the question,

x + 25 y = 4500... 1 x + 30 y = 5200... 2

Subtracting equation (1) from equation (2), we get,

⇒ 5 y = 700 ⇒ y = 140

Substituting the values of y in equation (1), we get,

⇒ x + 25140 = 4500 ⇒ x + 3500 = 4500 ⇒ x = 1000

Therefore, the fixed charge per month is ₹1,000 and the cost of food per day is ₹140. Hence, option 4 is correct.

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