Question

A reduction of 20% in the price of sugar enables a person to purchase 6 kg more for Rs. 240. What is the original price per kg of sugar?

• A. Rs. 10/kg
• B. Rs. 8/kg
• C. Rs. 6/kg
• D. Rs. 5/kg

Hint:

A 20% price cut lets the same money buy 5/4 times as much; the extra 1/4 of the original quantity equals 6 kg.

Answer 1

The Correct Option is A

Step 1: Set up the original and new price.
Let the original price be P per kg. After a 20% reduction, the new price is \(0.8P\) per kg.

Step 2: Find the quantities bought before and after.
Original quantity for Rs. 240 \(=\dfrac{240}{P}\) kg. New quantity for Rs. 240 \(=\dfrac{240}{0.8P}\) kg.

Step 3: Set up the equation for the extra quantity.
\(\dfrac{240}{0.8P}-\dfrac{240}{P}=6\).

Step 4: Simplify.
\(\dfrac{240}{0.8P}=\dfrac{300}{P}\), so \(\dfrac{300}{P}-\dfrac{240}{P}=6 \Rightarrow \dfrac{60}{P}=6 \Rightarrow P=10\).

Step 5: Final Answer.
The original price is Rs. 10 per kg, so option A is correct.