Question

A bookseller buys a number of books for rupees 1760. If he had bought 4 more books for the same amount each book would have cost rupees 22 less. How many books did he buy? ​

Answer 1

He buy 16 books.

Step-by-step explanation:

Consider the provided information.

Let the number of books he buy is x.

The cost of each book is: $\frac{1760}{x}$

If he had bought 4 more books for the same amount each book would have cost rupees 22 less.

Therefore,

$\frac{1760}{x}-\frac{1760}{x+4}=22$

$\frac{1}{x}-\frac{1}{x+4}=\frac{22}{1760}$

$\frac{x+4-x}{x(x+4)}=\frac{1}{80}$

$\frac{4}{x^2+4x}=\frac{1}{80}$

$x^2+4x-320=0$

$x^2+20x-16x-320=0$

$x(x+20)-16(x+20)=0$

$(x-16)(x+20)=0$

$x=16\ or\ x=-20$

The number of books can't be a negative number.

Therefore, he buy 16 books.

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the bookseller buy x books for 1760

Cost of each books = 1760/x

Cost of (x + 4) books = 1760/x + 4

According to the Question,

⇒ 1760/x - 1760/x + 4 = 22

⇒ 1/x - 1/x + 4 = 22/1760

⇒ (x + 4) - x/x(x + 4) = 1/80

⇒ 4/(x² + 4x) = 1/80

⇒ x² + 4x = 320

⇒ x² + 4x - 320 = 0

⇒ x² + 20x - 16x - 320 = 0

⇒ x(x + 20) - 16(x + 20) = 0

⇒ (x + 20) (x - 16) = 0

⇒ x + 20 = 0 or x - 16 = 0

⇒ x = - 20, 16 (As x can't be negative)

⇒ x = 16

Hence, the bookseller bought 16 books.

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