A trader marks his goods in such a way that after allowing 16% discount on the marked price, he still gains 26%. If the cost price of the goods is 318, then what is the marked price of the goods?

Options

A. 477
B. 456
C. 450
D. 427

Answer

To find the marked price of the goods, we can follow these steps:

### Step 1: Understand the relationship between cost price, selling price, and profit.
The profit percentage is calculated based on the cost price (CP). If the trader gains 26%, it means:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Where Profit = 26% of CP.

### Step 2: Calculate the Selling Price.
Given that the cost price (CP) is 318, we can calculate the selling price (SP) as follows:
\[ \text{Profit} = 26\% \text{ of } 318 = \frac{26}{100} \times 318 = 82.68 \]
Now, we can find the selling price:
\[ \text{SP} = \text{CP} + \text{Profit} = 318 + 82.68 = 400.68 \]

### Step 3: Relate Selling Price to Marked Price.
The trader gives a discount of 16% on the marked price (MP). Therefore, the selling price can also be expressed in terms of the marked price:
\[ \text{SP} = \text{MP} - \text{Discount} \]
Where Discount = 16% of MP.

### Step 4: Set up the equation.
The discount can be expressed as:
\[ \text{Discount} = 16\% \text{ of MP} = \frac{16}{100} \times \text{MP} = 0.16 \times \text{MP} \]
Thus, we can write:
\[ \text{SP} = \text{MP} - 0.16 \times \text{MP} = 0.84 \times \text{MP} \]

### Step 5: Substitute the Selling Price into the equation.
From Step 2, we have SP = 400.68. Therefore, we can substitute this into the equation from Step 4:
\[ 400.68 = 0.84 \times \text{MP} \]

### Step 6: Solve for Marked Price.
To find the marked price (MP), we can rearrange the equation:
\[ \text{MP} = \frac{400.68}{0.84} \]
Calculating this gives:
\[ \text{MP} = 476.07 \]

### Conclusion:
The marked price of the goods is approximately **476.07**.

---