Let the original price per kg of sugar be Rs x.
Then, the reduced price per kg = Rs \(\frac{4X}{5}\)
Quantity of sugar that can be bought for Rs 160 originally = Rs \(\frac{160}{X}\)
Quantity of sugar that can be bought for Rs 160 with reduced price = Rs \(\frac{160}{\frac{4X}{5}}\) = 160 x \(\frac{5}{4X}\)
Given, 160 x \(\frac{5}{4X}\) = \(\frac{160}{X}\)+ \(\frac{5}{2}\) \(\Rightarrow\) x = 16
\(\therefore\) Original price per kg = Rs 16.