Anirudh bought some books for Rs.60. If he had bought 5 more books for the same amount each book would have cost him 1 rupee less. Find the number of books bought by Anirudh and the price of each book.

Let's break down the problem step by step to find out how many books Anirudh bought and the price of each book.

Setting Up the Problem

Let the number of books Anirudh bought be x and the price of each book be p. According to the information given:

• The total cost of the books is Rs. 60, so we can write the equation: xp = 60.
• If he had bought 5 more books, the number of books would be x + 5, and the price per book would be p - 1.
• The total cost remains the same, leading to the equation: (x + 5)(p - 1) = 60.

Formulating the Equations

From the first equation, we can express p in terms of x:

p = 60/x

Now, substitute this value of p into the second equation:

(x + 5)(60/x - 1) = 60

Solving the Equation

Expanding the equation:

(x + 5)(60/x - 1) = 60

60 + 300/x - x - 5 = 60

Now, simplifying gives:

300/x - x - 5 = 0

Multiplying through by x to eliminate the fraction:

300 - x^2 - 5x = 0

Rearranging the Quadratic Equation

This can be rearranged to:

x^2 + 5x - 300 = 0

Finding the Roots

Now, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = 5, and c = -300.

Calculating the discriminant:

b² - 4ac = 5² - 4(1)(-300) = 25 + 1200 = 1225

Now, substituting into the formula:

x = (-5 ± √1225) / 2

x = (-5 ± 35) / 2

Calculating the Values

This gives us two potential solutions:

• x = 15 (valid since it must be positive)
• x = -20 (not valid)

Determining the Price

Now that we know x = 15, we can find the price per book:

p = 60/x = 60/15 = 4

Final Results

Anirudh bought 15 books, and each book cost Rs. 4.