After allowing a discount of 10% on the marked price of an article. it is sold for 450. Had the discount not been given, the profit would have been 25%. What is the 50% of the cost price (in Rs) of the article?

Options

A. 150
B. 200
C. 175
D. 250

Answer

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

### Step 1: Understand the given information
- Selling Price (SP) after a 10% discount = Rs 450
- Discount = 10%
- Profit without discount = 25%

### Step 2: Calculate the Marked Price (MP)
Since the selling price after a 10% discount is Rs 450, we can express this as:
\[ SP = MP \times (1 - \text{Discount}) \]
Substituting the values:
\[ 450 = MP \times (1 - 0.10) \]
\[ 450 = MP \times 0.90 \]
Now, solve for MP:
\[ MP = \frac{450}{0.90} \]
\[ MP = 500 \]

### Step 3: Calculate the Cost Price (CP)
We know that if no discount was given, the selling price would be equal to the marked price (MP). The profit is 25%, which means:
\[ SP = CP \times (1 + \text{Profit}) \]
Substituting the values:
\[ 500 = CP \times (1 + 0.25) \]
\[ 500 = CP \times 1.25 \]
Now, solve for CP:
\[ CP = \frac{500}{1.25} \]
\[ CP = 400 \]

### Step 4: Calculate 50% of the Cost Price
To find 50% of the cost price:
\[ 50\% \text{ of CP} = \frac{50}{100} \times CP \]
Substituting the value of CP:
\[ 50\% \text{ of CP} = \frac{50}{100} \times 400 \]
\[ 50\% \text{ of CP} = 200 \]

### Final Answer
Thus, 50% of the cost price of the article is Rs 200.

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