By selling an article for Rs 1170 a man allow 10% discount and earn 30% profit. If the article is sold at 0% discount what should be the profit %.

Options

A. 41`3/2`%
B. 45`4/9`%
C. 44`3/2`%
D. 44`4/9`%

Answer

To solve the problem step by step, we will follow the given information and calculate the necessary values.

### Step 1: Understand the Selling Price with Discount
The selling price of the article after allowing a 10% discount is Rs 1170.

### Step 2: Calculate the Market Price
Let the market price (MP) be \( x \). Since a 10% discount is given, the selling price (SP) can be expressed as:
\[ SP = MP - (10\% \text{ of } MP) = MP - 0.1 \times MP = 0.9 \times MP \]
Thus, we can write:
\[ 0.9x = 1170 \]
To find the market price, we solve for \( x \):
\[ x = \frac{1170}{0.9} = 1300 \]
So, the market price is Rs 1300.

### Step 3: Calculate the Cost Price
We know that the selling price of Rs 1170 gives a profit of 30%. Let the cost price (CP) be \( y \). The relationship between selling price, cost price, and profit can be expressed as:
\[ SP = CP + (30\% \text{ of } CP) = CP + 0.3 \times CP = 1.3 \times CP \]
Thus, we can write:
\[ 1170 = 1.3y \]
To find the cost price, we solve for \( y \):
\[ y = \frac{1170}{1.3} = 900 \]
So, the cost price is Rs 900.

### Step 4: Calculate Profit Percentage at 0% Discount
If the article is sold at 0% discount, the selling price will be equal to the market price, which we found to be Rs 1300.

Now, we can calculate the profit when sold at this price:
\[ \text{Profit} = SP - CP = 1300 - 900 = 400 \]

### Step 5: Calculate Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{400}{900} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \frac{400 \times 100}{900} = \frac{40000}{900} \approx 44.44\% \]

### Final Answer
Thus, the profit percentage when the article is sold at 0% discount is approximately **44.44%**.

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