# By a reduction of $1 per kg in the sugar price ,mahan can buy 1 kg more for$56. find the original price on 1 kg

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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.**

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