The price of sugar having gone down by 10%, a consumer can buy 5 kg more sugar for' 270. The difference between the original and reduced price per kg is :
चीनी की कीमत 10% कम हो जाने पर एक उपभोक्ता Rs 270 में 5 किग्रा. चीनी ज्यादा खरीद सकता है। तदनुसार, चीनी की मूल कीमत और कम हुई कीमत का अन्तर प्रति किग्रा.कितना है?

Options

A. A)62 p
B. B)60 p
C. C)75 p
D. D)53 p

Explanation

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

### Step 1: Understand the Price Change
Let the original price of sugar per kg be \( P \). After a 10% decrease, the new price becomes:
\[ \text{New Price} = P - 0.1P = 0.9P \]

### Step 2: Set Up the Equation for Quantity
According to the problem, the consumer can buy 5 kg more sugar for Rs 270 after the price decrease. Let’s denote the quantity of sugar bought at the original price as \( Q_1 \) and at the reduced price as \( Q_2 \):
\[ Q_1 = \frac{270}{P} \quad \text{(original quantity)} \]
\[ Q_2 = \frac{270}{0.9P} \quad \text{(new quantity)} \]

### Step 3: Relate the Quantities
From the problem, we know that:
\[ Q_2 = Q_1 + 5 \]
Substituting the expressions for \( Q_1 \) and \( Q_2 \):
\[ \frac{270}{0.9P} = \frac{270}{P} + 5 \]

### Step 4: Simplify the Equation
To eliminate the fractions, we can multiply through by \( 0.9P \):
\[ 270 = 0.9 \times 270 + 5 \times 0.9P \]
Calculating \( 0.9 \times 270 \):
\[ 270 = 243 + 4.5P \]

### Step 5: Solve for \( P \)
Rearranging the equation to isolate \( P \):
\[ 270 - 243 = 4.5P \]
\[ 27 = 4.5P \]
Dividing both sides by 4.5:
\[ P = \frac{27}{4.5} = 6 \text{ Rs/kg} \]

### Step 6: Calculate the Reduced Price
Now, we can find the reduced price:
\[ \text{Reduced Price} = 0.9P = 0.9 \times 6 = 5.4 \text{ Rs/kg} \]

### Step 7: Find the Difference in Price
Finally, the difference between the original price and the reduced price is:
\[ \text{Difference} = P - \text{Reduced Price} = 6 - 5.4 = 0.6 \text{ Rs/kg} \]

### Conclusion
Thus, the difference between the original and reduced price per kg is:
\[ \text{Difference} = 0.6 \text{ Rs/kg} \]