A discount of `2(1)/(2)%` is given to the customer on the marked price of an article. A man bought the article for Rs. 39. The marked price of the article is :

Options

A. Rs 42
B. Rs. 36.5
C. Rs 40
D. Rs 41.5

Answer

To find the marked price of the article after a discount of \(2.5\%\) (which is \(2\frac{1}{2}\%\)), we can follow these steps:

### Step 1: Understand the relationship between marked price, discount, and selling price
The selling price (SP) after applying the discount is given as Rs. 39. The discount is applied on the marked price (MP). The relationship can be expressed as:
\[ SP = MP - \text{Discount} \]
or
\[ SP = MP \times \left(1 - \frac{\text{Discount \%}}{100}\right) \]

### Step 2: Calculate the effective percentage after discount
The discount given is \(2.5\%\). Therefore, the effective percentage of the marked price that the customer pays is:
\[ 100\% - 2.5\% = 97.5\% \]

### Step 3: Set up the equation
Using the relationship from Step 1, we can express the selling price in terms of the marked price:
\[ 39 = MP \times \frac{97.5}{100} \]

### Step 4: Solve for the marked price
To find the marked price (MP), we rearrange the equation:
\[ MP = \frac{39 \times 100}{97.5} \]

### Step 5: Calculate the value
Now, we can calculate the marked price:
\[ MP = \frac{3900}{97.5} \]

### Step 6: Perform the division
To simplify \( \frac{3900}{97.5} \):
1. Multiply both numerator and denominator by 10 to eliminate the decimal:
\[ MP = \frac{39000}{975} \]
2. Now, divide \(39000\) by \(975\):
- \(975\) goes into \(3900\) approximately \(4\) times (since \(975 \times 4 = 3900\)).
- Therefore, \(MP = 40\).

### Conclusion
The marked price of the article is Rs. 40.

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