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
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.
∴80x−80x+4=1
⇒80(1x−1x+4)=1
⇒80{x+4−xx(x+4)}=1
⇒320x2+4x=1
⇒x2+4x=320
⇒x2+4x−320=0
⇒x2+20x−16x−320=0
⇒x(x+20)−16(x+20)=0
⇒(x+20)(x−16)=0
⇒x=−20 or, x=16⇒x=16 [∵x cannot be negative]
Hence, the number of books is 16.