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Let the original price = $ x per kg and he had bought y kg of sugar total price = $ xy = $56 -----------------(1) ⇒y = 56/x

if cost is reduced $1 per kg, new price of sugar = $ (x-1) he can buy = (y+1) kg total price = (x-1)(y+1)= 56 ---------------(2) ⇒xy + x - y -1 = 56 ⇒ 56 + x - y - 1 = 56 ⇒x - y - 1 = 0 ⇒ x - 56/x - 1 =0 ⇒x² - x - 56 = 0 or x = 8 and -7 (price can't be negative)