Due to a 25% increase in the price of rice per kilogram, a person is able to purchase 20 kg less for Rs. 400. What is the increased price of rice per kilogram?

Options

A. Rs.5
B. Rs.6
C. Rs.10
D. Rs. 4

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the problem
We know that due to a 25% increase in the price of rice, a person can buy 20 kg less rice for Rs. 400. We need to find the increased price of rice per kilogram.

### Step 2: Define the variables
Let the original price of rice per kilogram be \( P \).

### Step 3: Calculate the new price after the increase
Since the price increases by 25%, the new price \( P' \) can be calculated as:
\[ P' = P + 0.25P = 1.25P \]

### Step 4: Determine the quantity of rice purchased before the price increase
With the original price \( P \), the quantity of rice that could be purchased for Rs. 400 is:
\[ \text{Quantity before increase} = \frac{400}{P} \]

### Step 5: Determine the quantity of rice purchased after the price increase
After the price increase, the quantity of rice that can be purchased for Rs. 400 at the new price \( P' \) is:
\[ \text{Quantity after increase} = \frac{400}{1.25P} \]

### Step 6: Set up the equation based on the reduction in quantity
According to the problem, the person can buy 20 kg less rice after the price increase:
\[ \frac{400}{P} - \frac{400}{1.25P} = 20 \]

### Step 7: Simplify the equation
To simplify the left side of the equation, we need a common denominator:
\[ \frac{400 \cdot 1.25 - 400}{1.25P} = 20 \]
\[ \frac{500 - 400}{1.25P} = 20 \]
\[ \frac{100}{1.25P} = 20 \]

### Step 8: Solve for \( P \)
Cross-multiplying gives:
\[ 100 = 20 \cdot 1.25P \]
\[ 100 = 25P \]
\[ P = \frac{100}{25} = 4 \]

### Step 9: Calculate the increased price of rice per kilogram
Now that we have the original price \( P \), we can find the increased price \( P' \):
\[ P' = 1.25P = 1.25 \cdot 4 = 5 \]

### Final Answer
The increased price of rice per kilogram is **Rs. 5**.

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