# 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. - Mathematics

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

thereforeOriginal 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).

thereforeNew 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.

Concept: Real Numbers Examples and Solutions
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2011-2012 (March) Delhi Set 1

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