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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 Rs4500, whereas a student $B$ who takes food for 30 days, has to pay Rs 5200. Find the fixed charges per month and the cost of food per day.

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Monthly charges = Rs3000 and Cost of food per day = Rs90

Monthly charges = Rs1500 and Cost of food per day = Rs120

Monthly charges = Rs2000 and Cost of food per day = Rs100

Monthly charges = Rs1000 and Cost of food per day = Rs140

answer is D.

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Detailed Solution

Given that the student A takes food for 25 days and pays Rs. 4500 Student B takes food for 30 days and pays Rs. 5200
Let numerator be x and denominator be y, then,

x + 25 y = 4500 ⇒ x + 25 y − 4500 = 0 x + 30 y = 5200 ⇒ x + 30 y − 5200 = 0

On comparing the given equation with standard form, we get,

a 1 = 1, b 1 = 25, c 1 = − 4500 and a 2 = 1, b 2 = 30, c 2 = − 5200

Substituting the value of

a 1, b 1, c 1

and

a 2, b 2, c 2

, we get,

x = b 1 c 2 − b 2 c 1 a 1 b 2 − a 2 b 1 = − 130000 + 135000 30 − 25 = 1000 y = c 1 a 2 − c 2 a 1 a 1 b 2 − a 2 b 1 = − 4500 + 5200 30 − 25 = 140

Therefore, the monthly charges,

x = 1000

and cost of food per day,

y = 140

.
Hence, option (4) is correct.

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