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Solution :

Let the bookseller buy x books for Rs. 1760. <br> Then, cost of each book `= Rs. (1760)/(x).` <br> Again, cost of `(x+4)` books `= Rs. 1760` <br> `:." ""cost of each book, now "= Rs. (1760)/((x+4)).` <br> `:." "(1760)/(x)-(1760)/((x+4))=22` <br> `implies" "(1)/(x)-(1)/((x+4))=(22)/(1760)implies((x+4)-x)/(x(x+4))=(1)/(80)` <br> `implies" "(4)/((x^(2)+4x))=(1)/(80)impliesx^(2)+4x=320` <br> `implies" "x^(2)+4x-320=0impliesx^(2)+20x-16x-320=0` <br> `implies" "x(x+20)-16(x+20)=0implies(x+20)(x-16)=0` <br> `implies" "x+20=0" or "x-16=0impliesx=-20" or "x=16` <br> `implies" "x=16" "[because" number of books cannot be negative"]` <br> Hence, the bookseller bought 16 books.