The cost of the some books is RS 60 cost of every book is same if the book seller decrease the cost of the book by RS 1 one gets 5 books more for the same amount. What is the cost of each book and how many books are purchased Pl?

Question

Answer

Answer:

Each book costs Rs 4 and 15 books are purchased.

Step-by-step explanation:

Define x:

Let the number of books be x

Find the cost of 1 book:

Total cost of the books = Rs 60

Cost of 1 book = 60 � x = 60/x

Find the new price if it decrease by Rs 1:

New Price = 60/x - 1

Solve x:

Cost of book decreased by Rs 1, number of purchase increased by 5

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

60 + 300/x - x - 5 = 60

300/x - x - 5 = 0

300 - x� - 5x = 0

x� + 5x - 300 = 0

(x - 15)(x + 20) = 0

x = 15 or x = -20 (rejected, since books purchased cannot be negative)

Find the number of books purchased:

Number of books = x = 15

Find the cost of a book:

Total cost = Rs 60

Number of books = 15

Cost of a book = 60 � 15 = Rs 4

Answer

Problem

The cost of the some books is RS 60 cost of every book is same if the book seller decrease the cost of the book by RS 1 one gets 5 books more for the same amount. What is the cost of each book and how many books are purchased Pl? Explain in details.

Solution

Step 1: Understanding the problem

Let's first understand the problem statement. We are given the following information:

The cost of some books is RS 60.

The cost of every book is the same.

If the book seller decreases the cost of the book by RS 1, one gets 5 more books for the same amount.

Based on this information, we need to find out the cost of each book and the number of books purchased.

Step 2: Finding the initial cost of each book

Let's assume the initial cost of each book is x.

Therefore, the number of books that can be purchased for RS 60 is:

```
60/x
```

Step 3: Finding the new cost of each book

According to the problem statement, if the cost of each book is decreased by RS 1, 5 more books can be purchased for the same amount. Let's calculate the new cost of each book:

```
New cost of each book = x - 1
```

Therefore, the number of books that can be purchased for the same RS 60 with the new cost is:

```
60/(x-1)
```

According to the problem statement, this is 5 more than the number of books that can be purchased at the initial cost. Therefore, we can write:

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

Step 4: Solving the equation

Let's solve the equation:

```
60/x + 5 = 60/(x-1)
=> 60(x-1)/x(x-1) + 5x(x-1)/x(x-1) = 60x/x(x-1)
=> 60(x-1) + 5x(x-1) = 60x
=> 60x - 60 + 5x^2 - 5x = 60x
=> 5x^2 - 5x - 60 = 0
=> x^2 - x - 12 = 0
=> (x-4)(x+3) = 0
```

Therefore, x can be either 4 or -3. Since the cost of a book cannot be negative, we can discard -3 and conclude that:

```
x = 4
```

Therefore, the initial cost of each book is RS 4.

Step 5: Finding the number of books purchased

Now that we know the initial cost of each book, we can find the number of books that can be purchased for RS 60:

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