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 ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.

• A. ₹ 500, ₹ 50
• B. ₹ 300, ₹ 45
• C. ₹ 800, ₹ 20
• D. ₹ 400, ₹ 30

Answer 1

The correct option is D

₹ 400, ₹ 30

Let 'x' be the fixed monthly charges for the hostel and 'y' be the charge for food per day.
According to the question,
x + 20y = 1000 ... (i)
x + 26y = 1180 ... (ii)
Subtracting equation (i) from equation (ii), we get
6y = 180
$\Rightarrow$ $y=\frac{180}{6}=30$
Putting this value in equation (i), we get
x + 20 $\times$ 30 = 1000
$\Rightarrow$ x = 1000 - 600
$\Rightarrow$ x = 400
Hence, fixed charge = ₹ 400 and charge per day = ₹ 30.