As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs. 1,200. What Was the Original price of rice per kg?

The core idea is that the 25% hike in price means the person can buy 6 kg less rice for the same amount of money (Rs. 1,200). 1. Calculate the value of the 25% price hike in terms of money: If the price increased by 25%, then for the original quantity of rice, Rs. 1200 would no longer be enough. The extra money needed would be 25% of Rs. 1200, which is 0.25 * 1200 = Rs. 300. 2. This Rs. 300 is the cost of the 6 kg of rice that the person can no longer purchase at the new, increased price. 3. Therefore, the new price of rice per kg is Rs. 300 / 6 kg = Rs. 50 per kg. 4. Since the new price (Rs. 50) is a result of a 25% hike over the original price, the original price was 100% and the new price is 125% of the original price. 5. Let the original price be P. So, 1.25 * P = Rs. 50. 6. P = 50 / 1.25 = 50 / (5/4) = 50 * 4 / 5 = Rs. 40. Thus, the original price of rice per kg was Rs. 40. Analyzing the options: A) 30: If original price was 30, new price would be 30 * 1.25 = 37.5. Original quantity = 1200/30 = 40 kg. New quantity = 1200/37.5 = 32 kg. Difference = 8 kg (not 6 kg). B) 40: If original price was 40, new price would be 40 * 1.25 = 50. Original quantity = 1200/40 = 30 kg. New quantity = 1200/50 = 24 kg. Difference = 6 kg. This matches the problem statement. C) 50: If original price was 50, new price would be 50 * 1.25 = 62.5. Original quantity = 1200/50 = 24 kg. New quantity = 1200/62.5 = 19.2 kg. Difference = 4.8 kg (not 6 kg). D) 60: If original price was 60, new price would be 60 * 1.25 = 75. Original quantity = 1200/60 = 20 kg. New quantity = 1200/75 = 16 kg. Difference = 4 kg (not 6 kg). The final answer is B.