A dealer allows his customers a discount of 25% and still gains 25%. If an article costs Rs 1600 to the dealer, then its marked price (nearest to one rupee) is:

Options

A. Rs2000
B. Rs2050
C. Rs2667
D. Rs2600

Answer

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

### Step 1: Determine the Selling Price (SP)
The dealer allows a discount of 25% and still gains 25%. The cost price (CP) of the article is given as Rs 1600.

To find the selling price (SP), we can use the formula:
\[ SP = CP \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]

Substituting the values:
\[ SP = 1600 \times \left(1 + \frac{25}{100}\right) = 1600 \times 1.25 = 2000 \]

### Step 2: Calculate the Marked Price (MP)
Now that we have the selling price, we can calculate the marked price (MP) using the formula:
\[ MP = \frac{SP \times 100}{100 - \text{Discount \%}} \]

Substituting the values:
\[ MP = \frac{2000 \times 100}{100 - 25} = \frac{2000 \times 100}{75} \]

### Step 3: Simplify the Marked Price Calculation
Calculating further:
\[ MP = \frac{200000}{75} = 2666.67 \]

### Step 4: Round to the Nearest Rupee
Since we need the marked price nearest to one rupee, we round 2666.67 to:
\[ MP \approx 2667 \]

### Final Answer
The marked price of the article is Rs 2667.

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