Finding Fixed Charge and Cost per Day

Video Explanation

Question

A part of monthly hostel charges is fixed and the rest depends on the number of days food is taken. For 20 days, the charge is ₹1000. For 26 days, the charge is ₹1180. Find the fixed charge and cost of food per day.

Solution

Step 1: Let Variables

Let fixed charge = \(x\)

Let cost per day = \(y\)

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Step 2: Form Equations

For 20 days:

\[ x + 20y = 1000 \quad (1) \]

For 26 days:

\[ x + 26y = 1180 \quad (2) \]

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Step 3: Solve Linear Equations

Subtract (1) from (2):

\[ 6y = 180 \]

\[ y = 30 \]

Substitute into (1):

\[ x + 20(30) = 1000 \]

\[ x + 600 = 1000 \]

\[ x = 400 \]

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Step 4: Final Answer

\[ \text{Fixed charge} = ₹400,\quad \text{Cost per day} = ₹30 \]

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Verification

20 days: \(400 + 600 = 1000\) ✔

26 days: \(400 + 780 = 1180\) ✔