Question

A certain number of books were purchased for Rs.300.Five more books could have been purchased in the same amount, if each book was cheaper by Rs.10. The number was..........?

pls give a detailed ans.

Answer 1

$\textbf{Answer}$

Total amount spent = 300 Rs
Suppose price of each book = x Rs
=> Total number of books purchased = (300/x)

$\textbf{Now If,}$
Each book's price is cheaper by Rs 10,
$\textbf{5 more books can be purchased}$.
$\textbf{In this case,}$
Total amount spent = 300 Rs
Price of each book = (x - 10)
=> Number of books purchased = 300/(x - 10)

$\textbf{According to the question,}$
Total books purchased after reducing price is 5 greater than the books purchased at higher price in previous purchase.

=> 300/(x - 10) = 300/x + 5

=> 300/(x - 10) - 300/x = 5

=> 300{1/(x - 10) - 1/x} = 5

=> (x - x + 10)/(x)(x - 10) = 5/300

=>10/(x^2 - 10x) = 1/60

=> x^2 - 10x = 600

=> x^2 - 10x - 600 = 0

=> x^2 - 30x + 20x - 600 = 0

=> x(x - 30) + 20(x - 30) = 0

=> (x - 30) (x + 20) = 0

=> x = 30 or x = - 20

$\textbf{Since price can't be negative,}$

=> x = 30

$\textbf{Price of each book = 30 Rs}$
$\textbf{Total books purchased = 300}$
So the number of books purchased = 300/30

$\textbf{Number of books purchased = 10}$

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$