As a result of a 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? (UPSC 2020)
Question
As a result of a 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? (UPSC 2020)
Solution
Sure, let's solve this step by step:
Step 1: Let's assume the original price of rice per kg is Rs. x.
Step 2: After a 25% hike, the new price becomes 1.25x.
Step 3: According to the problem, with Rs. 1200, a person can buy 6 kg less rice at the new price. So, we can write the equation as: 1200/x - 1200/1.25x = 6.
Step 4: To simplify the equation, let's multiply all terms by x and 1.25x to get rid of the denominators: 1.251200 - 1200 = 6x1.25.
Step 5: Simplify further to get: 1500 - 1200 = 7.5x.
Step 6: So, 300 = 7.5x.
Step 7: Finally, solve for x by dividing both sides by 7.5: x = 300/7.5 = Rs. 40.
So, the original price of rice per kg was Rs. 40.
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