When the price of sugar decreases by 10%, a man could buy 1 kg more for Rs.270. Then the original price of sugar per kg is

Options

A. Rs. 25
B. Rs. 30
C. Rs. 27
D. Rs. 32

Answer

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

### Step 1: Define the original price of sugar
Let the original price of sugar per kg be \( x \) rupees.

### Step 2: Calculate the quantity of sugar that can be bought at the original price
If the man spends Rs. 270 at the original price, the quantity of sugar he can buy is:
\[ \text{Quantity at original price} = \frac{270}{x} \text{ kg} \]

### Step 3: Calculate the new price after a 10% decrease
When the price of sugar decreases by 10%, the new price becomes:
\[ \text{New price} = x - 0.1x = 0.9x \]

### Step 4: Calculate the quantity of sugar that can be bought at the new price
At the new price, the quantity of sugar he can buy for Rs. 270 is:
\[ \text{Quantity at new price} = \frac{270}{0.9x} = \frac{270 \times 10}{9x} = \frac{3000}{9x} \text{ kg} \]

### Step 5: Set up the equation based on the information given
According to the problem, the man can buy 1 kg more sugar at the new price than at the original price. Therefore, we can set up the equation:
\[ \frac{3000}{9x} = \frac{270}{x} + 1 \]

### Step 6: Clear the fractions by multiplying through by \( 9x \)
Multiplying through by \( 9x \) gives:
\[ 3000 = 2430 + 9x \]

### Step 7: Solve for \( x \)
Rearranging the equation:
\[ 3000 - 2430 = 9x \]
\[ 570 = 9x \]
\[ x = \frac{570}{9} = 63.33 \text{ (approximately)} \]

### Step 8: Finalize the answer
Since we are looking for the original price of sugar per kg, we round \( x \) to the nearest whole number if necessary. However, in this case, we can state that the original price of sugar per kg is approximately Rs. 63.33.

### Summary
The original price of sugar per kg is approximately Rs. 63.33.