A trader sells goods to a customer at a profit of `k%` over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus, his overall profit percentage is `25%`. Find the value of k?

Options

A. `8.33%`
B. `8.25%`
C. `10%`
D. `12.5%`

Answer

To find the value of \( k \) in the given problem, we will follow these steps:

### Step 1: Understand the Problem
The trader sells goods at a profit of \( k\% \) over the cost price (CP). However, he cheats the customer by giving only 880 grams instead of 1000 grams (1 kg). The overall profit percentage is 25%.

### Step 2: Set Up the Cost Price
Let the cost price of 1 kg (1000 grams) of goods be \( CP \). Therefore, the cost price of 880 grams is:
\[ \text{Cost Price of 880 grams} = \frac{880}{1000} \times CP = 0.88 \times CP \]

### Step 3: Calculate Selling Price with Profit
The trader sells the goods at a profit of \( k\% \). Thus, the selling price (SP) for 1 kg is:
\[ SP = CP + \left(\frac{k}{100} \times CP\right) = CP \left(1 + \frac{k}{100}\right) \]

### Step 4: Relate Selling Price to Overall Profit
Given that the overall profit percentage is 25%, we can express the selling price in terms of the cost price:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 5: Equate Selling Prices
Since the trader sells 880 grams for the same price as 1 kg, we can equate the selling price from both perspectives:
\[ CP \left(1 + \frac{k}{100}\right) = 1.25 \times CP \]

### Step 6: Simplify the Equation
We can cancel \( CP \) from both sides (assuming \( CP \neq 0 \)):
\[ 1 + \frac{k}{100} = 1.25 \]

### Step 7: Solve for \( k \)
Subtract 1 from both sides:
\[ \frac{k}{100} = 0.25 \]
Now, multiply both sides by 100:
\[ k = 25 \]

### Conclusion
The value of \( k \) is \( 25\% \).

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