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प्रश्न
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 25days, he has to pay Rs. 4550 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.
उत्तर
Let the fixed charges be Rs.x and the cost of food per day be Rs.y.
Then as per the question
x + 25y = 4500 ………(i)
x + 30y = 5200 ……..(ii)
Subtracting (i) from (ii), we get
5y = 700 ⇒ y = `700/5` = 140
Now, putting y = 140, we have
x + 25 × 140 = 4500
⇒x = 4500 – 3500 = 1000
Hence, the fixed charges be Rs.1000 and the cost of the food per day is Rs.140.
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