A bookseller buys a number of books for Rs. 1760. If he had bought 4 more books for the same amount, each book would have cost Rs. 22 less. How many books did he buy?

A bookseller buys a number of books for Rs. 1760. If he had bought 4 m

1.	A bookseller buys a number of books for Rs. 1760. If he had bought 4 more books for the same amount, each book would have cost Rs. 22 less. How many books did he buy?
Answer» Let the bookseller buy x books for Rs. 1760. Then, cost of each book `= Rs. (1760)/(x).` Again, cost of `(x+4)` books `= Rs. 1760` `:." ""cost of each book, now "= Rs. (1760)/((x+4)).` `:." "(1760)/(x)-(1760)/((x+4))=22` `implies" "(1)/(x)-(1)/((x+4))=(22)/(1760)implies((x+4)-x)/(x(x+4))=(1)/(80)` `implies" "(4)/((x^(2)+4x))=(1)/(80)impliesx^(2)+4x=320` `implies" "x^(2)+4x-320=0impliesx^(2)+20x-16x-320=0` `implies" "x(x+20)-16(x+20)=0implies(x+20)(x-16)=0` `implies" "x+20=0" or "x-16=0impliesx=-20" or "x=16` `implies" "x=16" "[because" number of books cannot be negative"]` Hence, the bookseller bought 16 books.