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

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

#### Solution

Let the number of books purchased by the shopkeeper be x.

Cost price of x books = Rs 80

`therefore`Original cost price of one book =Rs `80/"x"`

If the shopkeeper had purchased 4 more books, then the number of books purchased by him would be (x + 4).

`therefore`New cost price of one book Rs = `80/("x"+4)`

Given, Original cost price of one book − New cost price of one book = Rs 1

`therefore80/"x"-80/("x"+4)=1`

`rArr(80("x"+4)-80"x")/("x"("x"+4))=1`

`rArr80"x"+320-80"x"="x"("x"+4)`

`rArr"x"^2+4"x"=320`

`rArr"x"^2+4"x"=320=0`

`rArr"x"^2+20"x"-16"x"-320=0`

`rArr"x"("x"+20"x")-16("x"+20)=0`

`rArr("x"-16)("x"+20)=0`

`rArr"x"-16=0` or `"x"+20=0`

`rArr"x"-16=0` or `"x"+20=0`

`rArr"x"=16` 0r `"x"=-20`

`therefore "x"=16` .............(∵ Number of books cannot be negative)

Thus, the number of books purchased by the shopkeeper is 16.