Due to a 25% price hike in the price of 
rice, a person is able to purchase 20 kg less of rice for `
400. Find the initial price.

Let the initial price of rice per kg be \( x \) (in ₹).

Given that the person can buy 20 kg less rice after a 25% price hike with ₹400, let's set up the situation in equations:

1. **Initial condition (before the price hike):**
   The quantity of rice a person could buy for ₹400 is:
   \[
   \frac{400}{x} \text{ kg}
   \]
   
2. **After the price hike:**
   The new price per kg becomes \( 1.25x \) (since a 25% increase means multiplying the original price by 1.25). The new quantity of rice they can buy with ₹400 is:
   \[
   \frac{400}{1.25x} = \frac{400}{\frac{5x}{4}} = \frac{1600}{5x} \text{ kg}
   \]

3. **Condition given in the problem:**
   After the price hike, the person can purchase 20 kg less of rice. Thus, we have:
   \[
   \frac{400}{x} - \frac{1600}{5x} = 20
   \]

4. **Solve the equation:**
   Simplify the equation:
   \[
   \frac{400}{x} - \frac{320}{x} = 20
   \]
   \[
   \frac{80}{x} = 20
   \]
   Solving for \( x \):
   \[
   x = \frac{80}{20} = 4
   \]

Thus, the initial price of rice is ₹4 per kg.

Would you like further clarification or more details?

### Related Questions:
1. What would be the new price per kg after the price hike?
2. How much rice can the person buy after the price increase?
3. How would the equation change if the price hike was 30% instead of 25%?
4. What if the budget was ₹500 instead of ₹400?
5. How much less rice would the person buy if the price increase was 50%?

### Tip:
Always verify units and relationships in a word problem, as it helps in setting up accurate equations.

Due to a 25% price hike in the price of rice, a person is able to purchase 20 kg less of rice for ₹400. Find the initial price.

Learn how to calculate the initial price of rice when a 25% price hike results in a person purchasing 20 kg less rice for ₹400. This algebraic problem covers concepts like percentage increase and linear equations, suitable for Grades 8-10.

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