If the price of sugar is decreased by 18%, a person can buy 16.2 kg sugar more for Rs. 4500. What will be the new price (in Rs.) of sugar per kg.?

Options

A. 40
B. 60
C. 45
D. 50

Answer

To find the new price of sugar per kg after an 18% decrease, we can follow these steps:

### Step 1: Let the original price of sugar per kg be Rs. x.
- **Hint:** Define a variable for the original price to simplify calculations.

### Step 2: Calculate the new price after an 18% decrease.
- The decrease in price is 18% of x, which can be calculated as:
\[ \text{Decrease} = \frac{18}{100} \times x = 0.18x \]
- Therefore, the new price per kg (after the decrease) is:
\[ \text{New Price} = x - 0.18x = 0.82x \]
- **Hint:** Remember that a decrease means you subtract the percentage from the original value.

### Step 3: Determine how much sugar can be bought with Rs. 4500 at the original and new prices.
- At the original price, the amount of sugar that can be bought is:
\[ \text{Quantity at original price} = \frac{4500}{x} \]
- At the new price, the quantity of sugar that can be bought is:
\[ \text{Quantity at new price} = \frac{4500}{0.82x} \]
- **Hint:** Use the formula for quantity, which is total money divided by price per unit.

### Step 4: Set up the equation based on the information given in the question.
- According to the problem, the difference in quantity bought at the new price and the original price is 16.2 kg:
\[ \frac{4500}{0.82x} - \frac{4500}{x} = 16.2 \]
- **Hint:** This equation represents the additional quantity of sugar that can be purchased due to the price decrease.

### Step 5: Simplify the equation.
- Multiply through by \(0.82x\) to eliminate the denominators:
\[ 4500x - 4500 \times 0.82 = 16.2 \times 0.82x \]
- This simplifies to:
\[ 4500x - 3690 = 13.284x \]
- **Hint:** Distributing and combining like terms will help you isolate the variable.

### Step 6: Rearranging the equation.
- Rearranging gives:
\[ 4500x - 13.284x = 3690 \]
- Combining the x terms:
\[ 4486.716x = 3690 \]
- **Hint:** Keep your focus on isolating x to find its value.

### Step 7: Solve for x.
- Divide both sides by 4486.716:
\[ x = \frac{3690}{4486.716} \approx 0.822 \]
- **Hint:** Use a calculator for division to ensure accuracy.

### Step 8: Calculate the new price.
- The new price per kg is:
\[ \text{New Price} = 0.82x = 0.82 \times 0.822 \approx 0.674 \]
- **Hint:** Remember to multiply the original price by the factor you found to get the new price.

### Final Answer:
The new price of sugar per kg is approximately Rs. 0.674.