A product cost $100, 90% of the price being production cost,the remainder being tax, if the govt raises the tax by 50%, by how much in % will the factory have to reduce its production cost to keep he price still at $100

$10 is tax. 50% of that is $5, so reduce the cost by that much. What % of 90 is 5?

Just wondering -- where is the profit needed to make money?