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A shopkeeper buys some books for 80. If he had bought 4 more books for the same amount, each book would have cost ₹1 less. Find the number of books he bought

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Answer:

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Step-by-step EXPLANATION:

Let the shopkeeper buy x number of books.

According to the given condition cost of x books = Rs. 80

Therefore cost of each book = \large \frac{80}{x}

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =

\large \frac{80}{x + 4}

According to Question,

\large \frac{80}{x} - \frac{80}{x + 4} = 1 \\ \\ \large \frac{80(x + 4) - 80x}{x(x + 4)} = 1\\ \\ \large {x}^{2} - 20x - 16x - 320 = 0 \\ \\ \large (x - 16)(x + 20) = 0\\ \\ \large x = 16 \: \: or \: \: x = - 20

{Since no. of books cannot be negative, we ignore -20}

HENCE the shopkeeper brought 16 books


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