A man sold an article for Rs. 450, after allowing a discount of `16(2)/(3)%` on the printed price. What is that printed price ?

Options

A. Rs. 525
B. Rs. 530
C. Rs. 535
D. Rs. 540

Answer

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

### Step 1: Understand the Discount Percentage
The discount given is \(16 \frac{2}{3}\%\). We can convert this mixed fraction into an improper fraction:
\[ 16 \frac{2}{3} = \frac{50}{3}\% \]
This means the discount is \( \frac{50}{3} \% \).

### Step 2: Convert the Discount Percentage to a Fraction
To work with the discount in calculations, we convert the percentage to a fraction:
\[ \frac{50}{3} \% = \frac{50}{300} = \frac{1}{6} \]
This means that the discount is \( \frac{1}{6} \) of the marked price (MP).

### Step 3: Determine the Selling Price (SP) and Relation to Marked Price (MP)
The selling price (SP) after applying the discount can be represented as:
\[ SP = MP - \text{Discount} \]
Since the discount is \( \frac{1}{6} \) of the marked price, we can express this as:
\[ SP = MP - \frac{1}{6} MP = \frac{5}{6} MP \]

### Step 4: Set Up the Equation
We know from the problem that the selling price (SP) is Rs. 450. Therefore, we can set up the equation:
\[ \frac{5}{6} MP = 450 \]

### Step 5: Solve for the Marked Price (MP)
To find the marked price (MP), we can rearrange the equation:
\[ MP = 450 \times \frac{6}{5} \]
Calculating this gives:
\[ MP = 450 \times 1.2 = 540 \]

### Step 6: Conclusion
Thus, the printed price (marked price) of the article is Rs. 540.