Reading book in a library has a fixed charge for the first three days and an additional charge for each day thereafter. Shristi paid ₹ 27 for a book kept for seven days. While Bunty paid ₹ 21 for the book kept for five days.
(i) Find the fixed charge.
(ii) Find how much additional charge Shristi and Bunty paid.
(iii) Which mathematical concept is used in this problem ?
(iv) Which value does it depict ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let:
- \( X \) = Fixed charge for the first three days
- \( Y \) = Additional charge for each day thereafter

### Step 2: Set Up Equations
From the information given:
1. **For Shristi**: She paid ₹27 for 7 days.
- The first 3 days cost \( X \).
- The additional days are \( 7 - 3 = 4 \) days, costing \( 4Y \).
- Therefore, the equation becomes:
\[ X + 4Y = 27 \quad \text{(Equation 1)} \]

2. **For Bunty**: He paid ₹21 for 5 days.
- The first 3 days cost \( X \).
- The additional days are \( 5 - 3 = 2 \) days, costing \( 2Y \).
- Therefore, the equation becomes:
\[ X + 2Y = 21 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have the system of equations:
1. \( X + 4Y = 27 \)
2. \( X + 2Y = 21 \)

To eliminate \( X \), we can subtract Equation 2 from Equation 1:
\[ (X + 4Y) - (X + 2Y) = 27 - 21 \]
This simplifies to:
\[ 2Y = 6 \]
Now, divide both sides by 2:
\[ Y = 3 \]

### Step 4: Substitute \( Y \) Back to Find \( X \)
Now substitute \( Y = 3 \) back into Equation 2:
\[ X + 2(3) = 21 \]
This simplifies to:
\[ X + 6 = 21 \]
Now, subtract 6 from both sides:
\[ X = 15 \]

### Step 5: Summary of Charges
- Fixed charge \( X = 15 \)
- Additional charge \( Y = 3 \)

### Step 6: Calculate Additional Charges Paid by Shristi and Bunty
1. **For Shristi**: She paid for 4 additional days:
\[ \text{Additional charge} = 4Y = 4 \times 3 = 12 \]

2. **For Bunty**: He paid for 2 additional days:
\[ \text{Additional charge} = 2Y = 2 \times 3 = 6 \]

### Final Answers
(i) The fixed charge is ₹15.
(ii) Shristi paid an additional charge of ₹12, and Bunty paid an additional charge of ₹6.
(iii) The mathematical concept used is linear equations in two variables.
(iv) The value depicted is that reading is a good habit.