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A Part of Monthly Hostel Charges in a College Hostel 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 ₹4,500, Whereas a Student B Who Takes Food for 30 Days, He has to Pay ₹5,200. Find the Fixed Charges Per Month and the Cost of the Food Per Day.
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Here, the College Hostel charges a fixed fee for a month and the students need to pay an extra amount based on the number of days he/she gets food from the mess. So the total payable fee will vary according to the number of days a student took food for the month.
It is given that student “A” is paying ₹4,500 and he is taking food for 25 days. Student “B” is paying ₹5,200 and he is taking food for 30 days. Based on this, we need to find the fixed fee amount for one month and the cost of food per day.
Let’s assume the Fixed charges per month as ‘x’ and Cost of food per day as ‘y’
Then the equation for student “A” would become:
x + 25y = 4,500
The equation for student “B” would become:
x + 30y = 5,200
Let’s solve these equations by subtracting (B – A):
x + 30y – (x + 25y) = 5,200 – 4,500
x +30y – x – 25y = 700
5y = 700
y = 700 / 5
y = 140
So, the cost of food per day is ₹140.
Now, if you substitute ‘y = 140’ in any of the equations, you will get the value of ‘x’.
x + 25 (140) = 4,500
x + 3,500 = 4,500
x = 4,500 – 3,500
x = 1,000
So, the fixed charges per month is ₹1,000.
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Categories: Math
