Discounted Sugar Price Calculation

This problem involves finding the original and discounted price per kg of sugar. A 10% discount enabled buying 25 kg extra for ₹225.

Price Derivation Steps

Let the original price per kg be $P$. The discounted price per kg is $D = P \times (1 - 0.10) = 0.90 P$.

The total amount spent is $A = ₹225$.

Quantity at original price: $Q_P = A / P$. Quantity at discounted price: $Q_D = A / D$.

Given: $Q_D = Q_P + 25$.

Substitute into the equation: $ \frac{A}{D} = \frac{A}{P} + 25 $

Substitute values $A=225$ and $D=0.90 P$: $ \frac{225}{0.90 P} = \frac{225}{P} + 25 $ $ \frac{250}{P} = \frac{225}{P} + 25 $

Rearrange to solve for $P$: $ \frac{250}{P} - \frac{225}{P} = 25 $ $ \frac{25}{P} = 25 $

Solve for $P$: $ P = \frac{25}{25} = 1 $

The original price is ₹1 per kg.

Calculate the discounted price $D$: $ D = 0.90 \times P = 0.90 \times 1 = 0.90 $

The discounted price is ₹0.90 per kg, or 90 paise per kg.

Final Sugar Prices

The discounted price is 90 paise per kg.

The original price is ₹1 per kg.