A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should be his rate of mark up on an article costing Rs. 12?

Options

A. 0.2
B. `66 (2)/(3) %`
C. `30%`
D. `(100)/(3)%`

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Identify the Cost Price (CP)
The cost price of the article is given as:
\[ \text{CP} = 12 \, \text{Rs} \]

**Hint:** Remember that the cost price is the amount the trader spends to acquire the product.

### Step 2: Define Selling Price (SP)
Let the selling price be represented as \( x \).

**Hint:** The selling price is what the trader intends to sell the product for.

### Step 3: Calculate Expenses
The expenses are given as 15% of the selling price. Therefore, we can express the expenses as:
\[ \text{Expenses} = 0.15x \]

**Hint:** To find the expenses, multiply the selling price by the percentage given.

### Step 4: Calculate Profit
The trader wants a profit of 10% on the selling price. Thus, the profit can be expressed as:
\[ \text{Profit} = 0.10x \]

**Hint:** Profit is calculated as a percentage of the selling price.

### Step 5: Set Up the Equation
According to the problem, the selling price is equal to the cost price plus expenses plus profit:
\[ x = \text{CP} + \text{Expenses} + \text{Profit} \]
Substituting the values we have:
\[ x = 12 + 0.15x + 0.10x \]

### Step 6: Simplify the Equation
Combine the terms on the right side:
\[ x = 12 + 0.25x \]
Now, isolate \( x \):
\[ x - 0.25x = 12 \]
\[ 0.75x = 12 \]

### Step 7: Solve for Selling Price (SP)
Now, divide both sides by 0.75 to find \( x \):
\[ x = \frac{12}{0.75} = 16 \]

**Hint:** To isolate \( x \), you can divide both sides of the equation by the coefficient of \( x \).

### Step 8: Calculate Rate of Markup
The rate of markup is calculated using the formula:
\[ \text{Rate of Markup} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]
Substituting the values we found:
\[ \text{Rate of Markup} = \frac{16 - 12}{12} \times 100 \]
\[ = \frac{4}{12} \times 100 \]
\[ = \frac{1}{3} \times 100 = 33.33\% \]

### Step 9: Convert to Fraction
The rate of markup can also be expressed as:
\[ \frac{100}{3} \% \]

**Hint:** When calculating percentages, remember to convert fractions to percentages by multiplying by 100.

### Conclusion
The rate of markup on the article is:
\[ \text{Rate of Markup} = \frac{100}{3} \% \]

Thus, the correct answer is option D: \( \frac{100}{3} \% \).

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