A tradesman marks his goods at such a price that after allowing a discount of 15%, he maks a profit of 20%. What is the marked price of an article whose cost price is Rs. 170 ?

Options

A. Rs 240
B. Rs 260
C. Rs 220
D. Rs 200

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Selling Price (SP)
The cost price (CP) of the article is given as Rs. 170. The profit is 20% of the cost price.

To calculate the profit:
\[ \text{Profit} = 20\% \text{ of } CP = \frac{20}{100} \times 170 = 34 \]

Now, we can find the selling price (SP) using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} = 170 + 34 = 204 \]

### Step 2: Set up the equation for the Marked Price (MP)
Let the marked price (MP) be \( X \). The tradesman offers a discount of 15% on the marked price. The selling price after the discount can be expressed as:
\[ \text{SP} = \text{MP} - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = 15\% \text{ of } MP = \frac{15}{100} \times X = 0.15X \]

Thus, we can rewrite the selling price equation as:
\[ 204 = X - 0.15X \]
This simplifies to:
\[ 204 = 0.85X \]

### Step 3: Solve for the Marked Price (MP)
Now, we can solve for \( X \):
\[ X = \frac{204}{0.85} \]

Calculating this gives:
\[ X = 240 \]

### Conclusion
The marked price of the article is Rs. 240.