Fixed Charge and Charge Per Extra Day

Video Explanation

Question

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Solution

Step 1: Let the Variables

Let the fixed charge for first 3 days = Rs \(x\)

Let the charge for each extra day = Rs \(y\)

Step 2: Form the Equations

Saritha kept the book for 7 days. Extra days = \(7 – 3 = 4\)

\[ x + 4y = 27 \quad (1) \]

Susy kept the book for 5 days. Extra days = \(5 – 3 = 2\)

\[ x + 2y = 21 \quad (2) \]

Step 3: Solve by Elimination Method

Subtract equation (2) from equation (1):

\[ (x + 4y) – (x + 2y) = 27 – 21 \]

\[ 2y = 6 \]

\[ y = 3 \]

Step 4: Find the Value of x

Substitute \(y = 3\) in equation (2):

\[ x + 2(3) = 21 \]

\[ x + 6 = 21 \]

\[ x = 15 \]

Conclusion

Fixed charge for first 3 days:

\[ \boxed{Rs\; 15} \]

Charge for each extra day:

\[ \boxed{Rs\; 3} \]

Final Answer (For Exam)

Fixed charge = Rs 15
Charge per extra day = Rs 3