**(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.

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.

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^{st }case 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

X = 16 or X = – 20

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

Therefore , X – 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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