Fixed Charge Scenario of a Lending Library

In many lending libraries, the total charge for returning a book is composed of a fixed charge for the first few days and an additional charge for each day the book is kept beyond that period. This article explores how to determine the fixed and additional charges using a given scenario. We will use three different methods to solve the problem and determine the charges for a lending library.

Understanding the Scenario

Let's consider the following case: P paid Rs. 45 for a book kept for 7 days, while Q paid Rs. 25 for a book kept for 5 days. The library has a fixed charge for the first 3 days and an additional charge for each extra day.

Method 1: Standard Algebraic Equations

Let the fixed charge for 3 days be Rs. x and the additional charge per day for each extra day be Rs. y.

The total charge for P (7 days) can be represented as:

x 4y 45 …..(i)

The total charge for Q (5 days) can be represented as:

x 2y 25 ……(ii)

To find the value of y, we can subtract equation (ii) from equation (i):

(x 4y) - (x 2y) 45 - 25

This simplifies to:

2y 20

y 10

Substituting the value of y back into equation (ii):

x 2(10) 25

x 5

Hence, the fixed charge for the first 3 days is Rs. 5, and the additional charge per extra day is Rs. 10.

Method 2: Simplified Algebraic Equations

Let the fixed charge for 3 days be x and the charge per day be y.

The total charge for P (7 days), which includes 3 days of fixed charge and 4 days of additional charge, is:

x 4y 45 ……. (1)

The total charge for Q (5 days), which includes 3 days of fixed charge and 2 days of additional charge, is:

x 2y 25 ……. (2)

To find the value of y, we can subtract equation (2) from equation (1):

(x 4y) - (x 2y) 45 - 25

This simplifies to:

2y 20

y 10

Substituting the value of y back into equation (2):

x 2(10) 25

x 5

Hence, the fixed charge for the first 3 days is Rs. 5, and the additional charge per extra day is Rs. 10.

Method 3: Generalization and Simplification

Let the fixed charge for the first 3 days be x and the additional charge per day be y.

The total money paid by P can be represented as:

x 4y 45 ……. (1)

The total money paid by Q can be represented as:

x 2y 25 ……. (2)

To find the value of y, we can subtract equation (2) from equation (1):

(x 4y) - (x 2y) 45 - 25

This simplifies to:

2y 20

y 10

Substituting the value of y back into equation (2):

x 2(10) 25

x 5

Hence, the fixed charge for the first 3 days is Rs. 5, and the additional charge per extra day is Rs. 10.

Conclusion

In all three methods, we find that the fixed charge for the first 3 days is Rs. 5 and the additional charge for each extra day is Rs. 10. This information can be helpful for managing a lending library's charge system and understanding the financial implications of book lending periods.