A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for six days, while Anand paid Rs. 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.A) Rs. 13, Rs. 2B) Rs. 10, Rs. 3 C) Rs. 12, Rs. 9D) Rs. 14, Rs. 5

Let the fixed charge for the first two days be Rs. \( x \), and the additional charge for each extra day be Rs. \( y \).

### Step 1: Write equations for both scenarios

1. Latika paid Rs. 22 for 6 days. This includes the fixed charge for the first two days and an additional charge for 4 extra days:
\( x + 4y = 22 \)
Equation (1)

2. Anand paid Rs. 16 for 4 days. This includes the fixed charge for the first two days and an additional charge for 2 extra days:
\( x + 2y = 16 \)
Equation (2)

### Step 2: Subtract Equation (2) from Equation (1)

\[
(x + 4y) - (x + 2y) = 22 - 16
\]
\[
2y = 6
\]
\[
y = 3
\]

The additional charge for each extra day is Rs. 3.

### Step 3: Substitute \( y = 3 \) into Equation (2)

\[
x + 2(3) = 16
\]
\[
x + 6 = 16
\]
\[
x = 10
\]

The fixed charge for the first two days is Rs. 10.

### Step 4: Verify the solution

1. For Latika: \( x + 4y = 10 + 4(3) = 10 + 12 = 22 \) (Correct)
2. For Anand: \( x + 2y = 10 + 2(3) = 10 + 6 = 16 \) (Correct)

### Final Answer:
The fixed charge is Rs. 10, and the charge for each extra day is Rs. 3.
Correct option: B) Rs. 10, Rs. 3