a reduction of 20% in the price of sugar enables a housewife to purchase 6 kg. more for rs. 240. what is the original price per kg. of sugar?

Let the original price per kg of sugar be Rs. PPP.

A 20% reduction means the new price is 80% of PPP, or 0.8 P0.8P0.8P per kg.

For Rs. 240, she originally buys 240P\frac{240}{P}P240​ kg, but now buys 6 kg more at the reduced price: 2400.8P=240P+6\frac{240}{0.8P}=\frac{240}{P}+60.8P240​=P240​+6.

Step-by-Step Solution

1. Set up the equation :

2400.8P=240P+6\frac{240}{0.8P}=\frac{240}{P}+60.8P240​=P240​+6

2. Simplify left side : 2400.8P=240×1.25P=300P\frac{240}{0.8P}=\frac{240\times 1.25}{P}=\frac{300}{P}0.8P240​=P240×1.25​=P300​.

3. Substitute : 300P=240P+6\frac{300}{P}=\frac{240}{P}+6P300​=P240​+6.
4. Subtract fractions : 300−240P=6\frac{300-240}{P}=6P300−240​=6, so 60P=6\frac{60}{P}=6P60​=6.
5. Solve for PPP: P=606=10P=\frac{60}{6}=10P=660​=10.

The original price is Rs. 10 per kg.

Quick Verification Method

• 20% price drop = 1/5 reduction , so quantities shift 4:5 ratio (25% more quantity).

• 25% of original quantity = 6 kg → original quantity = 6×4=246\times 4=246×4=24 kg.

• Original price: 24024=10\frac{240}{24}=1024240​=10 Rs./kg.

Scenario| Price/kg| Quantity (kg)| Total Cost
---|---|---|---
Original| Rs. 10| 24| Rs. 240 1
Reduced (80%)| Rs. 8| 30| Rs. 240 4

TL;DR : Original price is Rs. 10 per kg.

Information gathered from public forums or data available on the internet and portrayed here.