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# A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs. 4500 as hostel charges whereas a student B, who takes food for 30 days, pays Rs. 5200 as hostel charges. Find the fixed charges and the cost of the food per day.

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An important and exam oriented question from linear equations in two variables in which we have find the fixed charges and the cost of the food per day. A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs. 4500 as hostel charges whereas a student B, who takes food for 30 days, pays Rs. 5200 as hostel charges.

Kindly solve the above problem by using the properties of linear equations

RS Aggarwal, Class 10, chapter 3E, question no 27

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1. Let the fixed charges be Rs.x and the cost of food per day be Rs.y.Â  Then as per the question

x + 25y = 4500 â€¦â€¦â€¦(i)

x + 30y = 5200 â€¦â€¦..(ii)

Subtracting (i) from (ii), we get

5y = 700

â‡’ y = 700/5 = 140

Now, putting y = 140, we have

x + 25 Ã— 140 = 4500

â‡’x = 4500 â€“ 3500 = 1000

Hence, the fixed charges be Rs.1000 and the cost of the food per day is Rs.140.

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