Solving the Sugar Price Reduction Problem
This problem involves calculating the original price per kg of sugar given a price reduction and the resulting increase in quantity purchased for a fixed amount.
Key Information Extraction
- Total Amount Spent: Rs. 200
- Price Reduction: 20%
- Increase in Quantity: 5 kg
- Goal: Find the original price per kg.
Mathematical Approach
Let the original price of sugar be $P$ Rs/kg. Let the original quantity purchased be $Q$ kg.
- From the total amount spent, we have the initial relationship: $ P \times Q = 200 \quad (1) $
- The price is reduced by 20%, so the new price is $P - 0.20P = 0.80P$ Rs/kg.
- With the reduced price, the person buys 5 kg more, so the new quantity is $Q + 5$ kg.
- The total amount spent remains Rs. 200, giving the second relationship: $ (0.80P) \times (Q + 5) = 200 \quad (2) $
- From equation (1), we can express $Q$ in terms of $P$: $ Q = \frac{200}{P} $
- Substitute this expression for $Q$ into equation (2): $ (0.80P) \times \left( \frac{200}{P} + 5 \right) = 200 $
- Simplify the equation: $ 0.80P \times \frac{200 + 5P}{P} = 200 $ $ 0.80 \times (200 + 5P) = 200 $
- Solve for $P$: $ 200 + 5P = \frac{200}{0.80} $ $ 200 + 5P = 250 $ $ 5P = 250 - 200 $ $ 5P = 50 $ $ P = \frac{50}{5} $ $ P = 10 $
Conclusion
The original price per kg of sugar is Rs. 10.
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