Step 1: Understand the relationship

A 20% reduction on the total amount of ₹160 gives the money saved which can buy 2.5 kg of sugar at the reduced price.

$20\% \text{ of } \text{₹}160 = \text{₹}32$

Step 2: Find the reduced price per kg

The savings of ₹32 enables the purchaser to buy 2.5 kg extra.

$\text{Reduced Price} = \frac{\text{₹}32}{2.5 \text{ kg}} = \text{₹}12.80 \text{ per kg}$

Step 3: Calculate the original price per kg

Since the reduced price is 80% of the original price ($P$), we can find $P$.

$0.80 \times P = 12.80 \implies P = \frac{12.80}{0.80} = \text{₹}16$

Step 4: Verify with direct formula

Using the standard shortcut formula for original price: $\frac{\text{Expenditure} \times \text{Percentage}}{\text{Extra Quantity} \times (100 - \text{Percentage})}$, we get $\frac{160 \times 20}{2.5 \times 80} = \frac{3200}{200} = 16$.

$\text{Original Price} = \text{₹}16 \text{ per kg}$