A discount of 20% in the price of rice enables X to buy 5 kg more rice for ₹100. What is the reduced price of rice per kg?

Options

A. ₹3
B. ₹2
C. ₹1
D. ₹4

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that a discount of 20% on the price of rice allows X to buy 5 kg more rice for ₹100. We need to find the reduced price of rice per kg.

### Step 2: Define Variables
Let:
- \( P \) = original price of rice per kg
- \( Q \) = original quantity of rice (in kg) that can be bought for ₹100

### Step 3: Write the Equation for Original Quantity
The original quantity of rice that can be bought for ₹100 is given by:
\[ Q = \frac{100}{P} \]

### Step 4: Calculate the Reduced Price
With a 20% discount, the new price per kg becomes:
\[ \text{Reduced Price} = P - 0.2P = 0.8P \]

### Step 5: Write the Equation for New Quantity
With the reduced price, the quantity of rice that can be bought for ₹100 increases by 5 kg:
\[ Q + 5 = \frac{100}{0.8P} \]

### Step 6: Substitute the Original Quantity
Substituting \( Q \) from Step 3 into the new quantity equation:
\[ \frac{100}{P} + 5 = \frac{100}{0.8P} \]

### Step 7: Simplify the Equation
To eliminate the fractions, multiply through by \( P \) and \( 0.8P \):
\[ 100 \cdot 0.8 + 5 \cdot 0.8P = 100 \]
\[ 80 + 4P = 100 \]

### Step 8: Solve for P
Rearranging gives:
\[ 4P = 100 - 80 \]
\[ 4P = 20 \]
\[ P = 5 \]

### Step 9: Find the Reduced Price
Now, we can find the reduced price:
\[ \text{Reduced Price} = 0.8P = 0.8 \times 5 = 4 \]

### Conclusion
The reduced price of rice per kg is ₹4.