Sugar Price Reduction Problem Explained

This question asks for the reduced price per kg of sugar when a 10% price decrease allows purchasing more quantity for the same total cost.

Calculating the Reduced Price Per Kilogram

Let the original price per kg be \(P_{orig}\) and the reduced price per kg be \(P_{red}\).

Given:

• Total amount spent = \(₹2790\)
• Price reduction = 10%
• Extra quantity bought = 6.2 kg

The reduced price is 10% less than the original price:

\(P_{red} = P_{orig} \times (1 - 0.10) = 0.9 \times P_{orig}\)

The quantity that can be bought is inversely proportional to the price for a fixed total amount.

Original Quantity (\(Q_{orig}\)) = \(\frac{2790}{P_{orig}}\)

New Quantity (\(Q_{new}\)) = \(\frac{2790}{P_{red}} = \frac{2790}{0.9 \times P_{orig}}\)

The difference in quantity is given:

\(Q_{new} - Q_{orig} = 6.2\)

Substituting the quantity expressions:

\(\frac{2790}{0.9 \times P_{orig}} - \frac{2790}{P_{orig}} = 6.2\)

Factor out \(\frac{2790}{P_{orig}}\):

\(\frac{2790}{P_{orig}} \left( \frac{1}{0.9} - 1 \right) = 6.2\)

Simplify the term in parenthesis:

\(\frac{2790}{P_{orig}} \left( \frac{10}{9} - \frac{9}{9} \right) = 6.2\)

\(\frac{2790}{P_{orig}} \left( \frac{1}{9} \right) = 6.2\)

\(\frac{310}{P_{orig}} = 6.2\)

Solve for the original price:

\(P_{orig} = \frac{310}{6.2} = 50\)

The original price was \(₹50\) per kg.

Now, calculate the reduced price:

\(P_{red} = 0.9 \times P_{orig} = 0.9 \times 50 = 45\)

The reduced price per kilogram is \(₹45\).