A person is able to buy 2 kg more for Rs.198, due to a reduction of 8% in the price of rice. What is the difference between the original and the reduced rate of rice per kg?
Question
A person is able to buy 2 kg more for Rs.198, due to a reduction of 8% in the price of rice. What is the difference between the original and the reduced rate of rice per kg?
Solution
Step 1: Let's assume the original price of rice per kg is Rs. x.
Step 2: After an 8% reduction, the new price per kg becomes Rs. (100% - 8%)x = 92%x.
Step 3: According to the problem, the person is able to buy 2 kg more rice for Rs.198 due to this reduction. This means the difference in price for 2 kg rice is Rs.198.
Step 4: So, we can set up the equation: 2x - 2(92%x) = 198.
Step 5: Simplify the equation: 2x - 1.84x = 198.
Step 6: Solve for x: 0.16x = 198.
Step 7: Find the value of x: x = 198 / 0.16 = Rs.1237.5.
Step 8: So, the original price per kg of rice was Rs.1237.5.
Step 9: The reduced price per kg of rice is 92% of the original price, which is 0.92 * 1237.5 = Rs.1138.5.
Step 10: The difference between the original and the reduced rate of rice per kg is Rs.1237.5 - Rs.1138.5 = Rs.99.
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