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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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Rs. 200 and Rs. 20

Rs. 400 and Rs. 40

Rs. 300 and Rs. 30

Rs. 400 and Rs. 30

answer is D.

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Detailed Solution

Suppose the fixed charge = Rs. x
The variable charge = y /day.
When A takes food for 20 days, the hostel charges = 1000. Thus,

x + 20 y = 1000

x = 1000 - 20 y

…………. (1)
When B takes food for 12 days, hostel charge= Rs 1180

x + 26 y = 1180

…………………(2)
Put

x

value in equation (2),

x + 26 y = 1180

\Rightarrow 1000 - 20 y + 26 y = 1180

\Rightarrow - 20 y + 26 y = 1180 - 1000

\Rightarrow 6 y = 180

\Rightarrow y = \frac{180}{6}

\Rightarrow y = 30

Now, put the value of y in equation (1)

x = 1000 - (20 \times 30)

x = 1000 - 600

x = 400

Therefore,
Fixed charge,

x = 400

Cost of food per day

= 30

Correct option is 4.

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