Finding Fixed Charge and Extra Day Rent

Video Explanation

Question

A shopkeeper charges a fixed amount for the first 2 days and an additional charge per day after that. Latika pays ₹22 for 6 days. Anand pays ₹16 for 4 days. Find the fixed charge and the charge per extra day.

Solution

Step 1: Let Variables

Let fixed charge (for first 2 days) = \(x\)

Let charge per extra day = \(y\)

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Step 2: Form Equations

Latika (6 days → 4 extra days):

\[ x + 4y = 22 \quad (1) \]

Anand (4 days → 2 extra days):

\[ x + 2y = 16 \quad (2) \]

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Step 3: Solve Linear Equations

Subtract (2) from (1):

\[ 2y = 6 \]

\[ y = 3 \]

Substitute into (2):

\[ x + 2(3) = 16 \]

\[ x + 6 = 16 \]

\[ x = 10 \]

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Step 4: Final Answer

\[ \text{Fixed charge} = ₹10,\quad \text{Charge per extra day} = ₹3 \]

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Verification

6 days: \(10 + 12 = 22\) ✔

4 days: \(10 + 6 = 16\) ✔