A reduction of 20% in the price of sugar enables a purchase to obtain 2.5 kg more for Rs. 160. The original price per kg of sugar is:

Correct option is B

Given:
A reduction of 20% in the price of sugar
purchase to obtain 2.5 kg more for Rs. 160
Solution:
Let the original price per kg of sugar is Rs. x
then the reduced price per kg = $$x \times \frac{80}{100} = \frac{4x}{5}$$​​
Quantity of sugar that can be bought for Rs. 160 originally = $$\frac{160}{x}$$​​
Quantity of sugar that can be bought for Rs. 160 with reduced price = $$= \frac{160}{\left( \frac{4x}{5} \right)} = \frac{800}{4x}$$​​
According to the question,
​$$\Rightarrow \frac{800}{4x} = \frac{160}{x} + 2.5\\\ \\\Rightarrow \frac{800}{4x} - \frac{160}{x} = 2.5\\\ \\\Rightarrow \frac{800 - 640}{4x} = 2.5\\\ \\\Rightarrow \frac{160}{4x} = 2.5\\\Rightarrow 160 = 10x\\\Rightarrow x = 16\\$$​​
∴ The original price per kg for sugar is Rs. 16.

Alternate Solution:

$$\text{Price }\quad\quad \quad \quad 5 \quad 4\\\text{Consumption }\quad \ 4 \quad 5$$ 

1 unit increase = 2.5 kg
So, Original Consumption = 10 kg
So, The original price per kg for sugar = $$\frac{160}{10} = 16$$ per kg​