Question

# 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 ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.

A

₹ 500, ₹ 50

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B

₹ 300, ₹ 45

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C

₹ 800, ₹ 20

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D

₹ 400, ₹ 30

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Solution

## The correct option is D ₹ 400, ₹ 30 Let 'x' be the fixed monthly charges for the hostel and 'y' be the charge for food per day. According to the question, x + 20y = 1000 ... (i) x + 26y = 1180 ... (ii) Subtracting equation (i) from equation (ii), we get 6y = 180 ⇒ y=1806=30 Putting this value in equation (i), we get x + 20 × 30 = 1000 ⇒ x = 1000 - 600 ⇒ x = 400 Hence, fixed charge = ₹ 400 and charge per day = ₹ 30.

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