Question

A shopkeeper buys a number of books for Rs 1200 if he had bought 10 more books for the same amount each book would have cost to cost Rs 20 less how many books did he buy

Answer 1

let the no. of books that he bought be x.

total price=no. of books × price of 1 book
1200=x × price of one book
so,
price of one book
$= \frac{1200}{x}$

he buys 10 more books

then the price of one book
$= \frac{1200}{x + 10}$
by the given condition,


$\frac{1200}{x} - \frac{1200}{x + 10} = 20$

$1200(\frac{1}{x} - \frac{1}{x + 10} ) = 20$


$( \frac{1}{x} - \frac{1}{x + 10} ) = \frac{20}{1200}$


$( \frac{1}{x} - \frac{1}{x + 10} ) = \frac{1}{60}$


$\frac{x + 10 - x}{x(x + 10)} = \frac{1}{60}$

$\frac{10}{ {x}^{2} + 10x } = \frac{1}{60}$


${x}^{2} + 10x = 10 \times 60$

${x}^{2} + 10x = 600$


${x}^{2} + 10x - 600 = 0$

by factorization method


${x}^{2} + 30x - 20x - 600 = 0$


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


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

therefore,

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

x+30=0 Or x-20=0

x=-30 or x=20

but x=-30 is not acceptable .


so,
x=20

THE NO. OF BOOKS HE Bought ARE 20.

hope this helps!!!

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the number of books bought be x.

According to the Question,

⇒ 1200/x - 1200/x + 10 = 20

⇒ 1200[1/x - 1/x + 10] = 20

⇒ x - 10 - x/x(x + 10) = 1/60

⇒ x² + 10 - x = x² + 10x/60

⇒ x² + 10x = 600

⇒ x² + 10x - 600 = 0

⇒ x(x + 30) - 20(x + 30) = 0

⇒ (x - 20) (x + 30) = 0

⇒ x = 20, - 30 (As x can't be negative)

⇒ x = 20

Number of books = x = 20

Hence, the number of books are 20.