Subjective Type

Represent the following situations mathematically: A shopkeeper buys a number of books for Rs.80.If he had bought four more books for the same amount, the book would have cost Re.1 less.

Solution

Let 'x' be the number of books bought by the shopkeeper. $$\therefore $$Cost of one book = Rs. $$80 \div x$$
[$$\because$$ the total cost of books is Rs. 80]
$$\therefore$$ Cost of one book when he buys 4 more books for same rate = Rs.$$ 80 \div (x + 4)$$.
When he buys four more books for the same amount; it will cost Re. 1 per book less than the previous.
$$\therefore 80 \div (x + 4) = (80 \div x) - 1$$
$$\Rightarrow \dfrac{80}{x+4}=\dfrac{80}{x}-1$$
$$ \Rightarrow 80x=80x-x^2+320-4x$$
$$\Rightarrow x^2+4x+320=0$$

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