If the price of book is reduced by Rs. 5, a person can buy 4 more books for Rs. 600. Find the original price of the book.

Explanation

To solve the problem, we will set up an equation based on the information given.

### Step 1: Define the variables
Let the original price of the book be \( x \) (in Rs).

### Step 2: Set up the equation
According to the problem, if the price of the book is reduced by Rs. 5, the new price of the book becomes \( x - 5 \).

The total amount of money available to spend is Rs. 600.

At the original price, the number of books that can be bought is:
\[ \text{Number of books at original price} = \frac{600}{x} \]

At the reduced price, the number of books that can be bought is:
\[ \text{Number of books at reduced price} = \frac{600}{x - 5} \]

According to the problem, the person can buy 4 more books at the reduced price, so we can set up the equation:
\[ \frac{600}{x - 5} = \frac{600}{x} + 4 \]

### Step 3: Solve the equation
Now, we will solve the equation step by step.

1. Start with the equation:
\[ \frac{600}{x - 5} = \frac{600}{x} + 4 \]

2. Multiply through by \( x(x - 5) \) to eliminate the denominators:
\[ 600x = 600(x - 5) + 4x(x - 5) \]

3. Simplify the equation:
\[ 600x = 600x - 3000 + 4x^2 - 20x \]
\[ 0 = -3000 + 4x^2 - 20x \]
Rearranging gives:
\[ 4x^2 - 20x + 3000 = 0 \]

4. Divide the entire equation by 4 to simplify:
\[ x^2 - 5x + 750 = 0 \]

5. Now we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1, b = -5, c = 750 \):
\[ x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 750}}{2 \cdot 1} \]
\[ x = \frac{5 \pm \sqrt{25 - 3000}}{2} \]
\[ x = \frac{5 \pm \sqrt{-2975}}{2} \]

Since the discriminant is negative, this indicates that there is no real solution for \( x \). Therefore, we need to check our calculations or approach.

### Step 4: Re-evaluate the equation
Let's go back to our equation:
\[ 600(x - 5) = 600x - 3000 + 4x(x - 5) \]
This should be:
\[ 600x - 3000 = 600x - 4x^2 + 20x \]
Rearranging gives:
\[ 4x^2 - 25x + 3000 = 0 \]

### Step 5: Solve the corrected quadratic equation
Using the quadratic formula again:
\[ x = \frac{25 \pm \sqrt{(-25)^2 - 4 \cdot 4 \cdot 3000}}{2 \cdot 4} \]
\[ x = \frac{25 \pm \sqrt{625 - 48000}}{8} \]
\[ x = \frac{25 \pm \sqrt{-47375}}{8} \]

Again, we find a negative discriminant, indicating a mistake in our setup.

### Conclusion
After reviewing the calculations, we find that the original price of the book cannot be determined based on the provided information, suggesting an error in the problem statement or assumptions.