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 Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
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 Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
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In problems involving fixed costs and variable costs, set up a system of equations and solve for both variables.
Updated On: Aug 18, 2025
- 300, 30
- 400, 40
- 200, 20
- 400, 30
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The Correct Option is D
Solution and Explanation
Let the fixed charges be \( F \) and the cost of food per day be \( C \).
For Student A:
\[
F + 20C = 1000
\]
For Student B:
\[
F + 26C = 1180
\]
Subtracting the first equation from the second:
\[
(F + 26C) - (F + 20C) = 1180 - 1000
\]
\[
6C = 180 \quad \Rightarrow \quad C = 30
\]
Substitute \( C = 30 \) into the first equation:
\[
F + 20(30) = 1000 \quad \Rightarrow \quad F + 600 = 1000 \quad \Rightarrow \quad F = 400
\]
Thus, the fixed charges are Rs. 400 and the cost per day is Rs. 30.
- Option (A) 300, 30: This is incorrect, as the fixed charges are not 300.
- Option (B) 400, 40: This is incorrect, the cost of food per day is 30, not 40.
- Option (C) 200, 20: This is incorrect, as both the fixed charges and the food cost are not as low as this.
- Option (A) 300, 30: This is incorrect, as the fixed charges are not 300.
- Option (B) 400, 40: This is incorrect, the cost of food per day is 30, not 40.
- Option (C) 200, 20: This is incorrect, as both the fixed charges and the food cost are not as low as this.
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