A shopkeeper buys a number of books for Rs. 80. If he had bought 4

(Q) A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?

Ans:

Let the shopkeeper buy X number of books.

By the given condition, cost of X books = Rs. 80

Therefore, in this 1^st case, cost of each book = Rs. $\frac{80}{\times}$

Next, in 2^nd case, he bought 4 more books for same amount,

therefore, total number of books in the 2^nd case = X + 4

and, cost of each book in 2^nd case = Rs. $\frac{80}{\times + 4}$

Since it is given, that the cost of one book in 2^nd case is reduced by 1 Rupee

or we can say that cost of one book in 1^stcase is 1 rupee more than the cost of one book in 2^nd case

Therefore, Cost of Book in 1^st case – Cost of Book in 2^nd case = 1

$\therefore \frac{80}{\times} - \frac{80}{\times + 4} = 1$

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

$\Rightarrow 80 [\frac{{\cancel \times}+4-{\cancel \times}}{\times(\times + 4)}]=1$

$\Rightarrow \frac{320}{\times^2 + 4\times}=1$

$\Rightarrow \times^2 + 4\times - 320 = 0$

$\Rightarrow \times^2 + 20\times - 16\times - 320 = 0$

$\Rightarrow \times (\times + 20) - 16(\times + 20) = 0$

$\Rightarrow (\times - 16)(\times + 20) = 0$

$\Rightarrow$ X = 16 or X = – 20

Here, we reject X = – 20, because number of books can not be a negative number.

Therefore , X $\neq$ – 20, and only X = 16

Hence, the shopkeeper bought 16 books.

Check:

Shopkeeper bought 16 books for Rs. 80, hence cost of one book is Rs. 5

Next, he bought 4 more books i.e. 16 + 4 = 20 books for same amount of Rs. 80, hence cost of one book is Rs. 4

Since, here Rs. 4 is Rs. 1 less than Rs. 5, hence our answer is correct.

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