Rahul professes to lose 16% on selling sugar and uses a weight of 680 gm instead of 1 kg. What is the total profit percentage?

Options

A. `23.52`
B. 16
C. `28.57`
D. `19.24`

Answer

To solve the problem step by step, we will break down the calculations involved in determining the total profit percentage that Rahul makes when selling sugar.

### Step 1: Determine the Cost Price (CP) of 1 kg of sugar
Assume the price of 1 kg (1000 grams) of sugar is ₹1000.

**Hint:** Always start by defining the cost of the full quantity to understand the unit price.

### Step 2: Calculate the Selling Price (SP) after the loss
Rahul claims to lose 16% on selling sugar. Therefore, the Selling Price (SP) after a 16% loss can be calculated as follows:
- Loss = 16% of CP = 16% of ₹1000 = ₹160
- SP = CP - Loss = ₹1000 - ₹160 = ₹840

**Hint:** Remember that the Selling Price is always calculated after deducting the loss from the Cost Price.

### Step 3: Calculate the Cost Price (CP) for 680 grams of sugar
Since the price of 1 gram of sugar is ₹1 (from Step 1), the Cost Price for 680 grams is:
- CP of 680 grams = 680 grams × ₹1/gram = ₹680

**Hint:** When calculating the cost for a smaller quantity, multiply the unit price by the number of units.

### Step 4: Calculate the Profit
Now, we find the profit made by selling 680 grams of sugar:
- Profit = SP - CP = ₹840 - ₹680 = ₹160

**Hint:** Profit is simply the difference between the Selling Price and the Cost Price.

### Step 5: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{160}{680} \right) \times 100 \]

### Step 6: Simplify the Profit Percentage Calculation
Now, simplify the fraction:
- Dividing both numerator and denominator by 40:
\[ \frac{160}{680} = \frac{4}{17} \]
Now calculate the percentage:
\[ \text{Profit Percentage} = \left( \frac{4}{17} \right) \times 100 \approx 23.52\% \]

**Hint:** When calculating percentages, simplify the fraction first for easier calculations.

### Conclusion
The total profit percentage that Rahul makes by selling sugar is approximately **23.52%**.