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2014-10-24T14:31:09+05:30

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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)

So the original cost was $8 per kg.
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