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Question

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. He bought ___ books.


A

16

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B

18

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C

14

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D

12

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Solution

The correct option is A

16


Let the number of books bought be x. Then,

Cost of x books =80 Cost of one book =80x

If the number of books bought is x+4, then

Cost of one book =80x+4

It is given that the cost of one book is reduced by one rupee.

80x80x+4=1

80(1x1x+4)=1

80{x+4xx(x+4)}=1

320x2+4x=1

x2+4x=320

x2+4x320=0

x2+20x16x320=0

x(x+20)16(x+20)=0

(x+20)(x16)=0

x=20 or, x=16x=16 [x cannot be negative]

Hence, the number of books is 16.


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