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.

Let the number of books bought by the shopkeeper be x.
Price of x books = Rs.80 ⇒ Price of 1 book = 80/x — (1)
Now, if the number of books had been (x+4)
Price of x+4 books = 80 ⇒ Price of 1 book = 80/(x+4) — (2)
Now, according to the question, equation (1) - (2) = 1.
i.e., 80/x - 80/(x+4) = 1
⇒ 320/(x²+4x) = 1
x² + 4x - 320 = 0
⇒ x² + 20x - 16x - 320 = 0
⇒ x(x+20) - 16(x+20) = 0
⇒ (x-16)(x+20) = 0
⇒ x = 16 or x = -20. But the number of books can never be negative.
Therefore the number of books he bought = 16.