The price of. Sugar having go down by 10%, a consumer can buy 5 kg more sugar for `Rs 270`. The difference between the original and reduced price per kg is :

Options

A. 75 paise
B. 53 paise
C. 62 paise
D. 60 paise

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
The price of sugar has decreased by 10%, allowing a consumer to buy 5 kg more sugar for Rs 270. We need to find the difference between the original price per kg and the reduced price per kg.

### Step 2: Define Variables
Let the original price of sugar per kg be \( P \) (in Rs). After a 10% decrease, the new price per kg becomes:
\[ \text{New Price} = P - 0.1P = 0.9P \]

### Step 3: Determine the Quantity of Sugar Bought
For Rs 270, the quantity of sugar that can be bought at the original price is:
\[ \text{Quantity at Original Price} = \frac{270}{P} \]
At the reduced price, the quantity of sugar that can be bought is:
\[ \text{Quantity at Reduced Price} = \frac{270}{0.9P} \]

### Step 4: Set Up the Equation
According to the problem, the difference in quantity is 5 kg:
\[ \frac{270}{0.9P} - \frac{270}{P} = 5 \]

### Step 5: Simplify the Equation
To simplify the left-hand side, we can find a common denominator:
\[ \frac{270P - 270 \cdot 0.9P}{0.9P^2} = 5 \]
This simplifies to:
\[ \frac{270(1 - 0.9)}{0.9P^2} = 5 \]
\[ \frac{270 \cdot 0.1}{0.9P^2} = 5 \]
\[ \frac{27}{P^2} = 5 \]

### Step 6: Solve for \( P^2 \)
Cross-multiplying gives:
\[ 27 = 5P^2 \]
\[ P^2 = \frac{27}{5} \]
\[ P = \sqrt{\frac{27}{5}} = \frac{3\sqrt{3}}{\sqrt{5}} \approx 3.464 \]

### Step 7: Calculate the Reduced Price
Now, we can find the reduced price:
\[ \text{Reduced Price} = 0.9P = 0.9 \cdot \frac{3\sqrt{3}}{\sqrt{5}} \approx 3.118 \]

### Step 8: Find the Difference
Now, we find the difference between the original and reduced price:
\[ \text{Difference} = P - 0.9P = 0.1P = 0.1 \cdot \frac{3\sqrt{3}}{\sqrt{5}} \approx 0.346 \]

### Step 9: Convert to Money
To express the difference in terms of money, we multiply by 100 (since 1 Rs = 100 paise):
\[ \text{Difference in paise} = 0.346 \cdot 100 \approx 34.6 \]

### Conclusion
The difference between the original and reduced price per kg is approximately Rs 0.346, or 34.6 paise.

---