A man sold his article at 35% gain. If he sold articles for Rs. 50 more, he would have gained 45% , If he wants a profit of 56% then what should be the marked price of the article if there is no discount offered?

Options

A. Rs. 780
B. Rs. 886
C. Rs. 892
D. Rs. 986

Answer

To solve the problem step by step, we will first determine the cost price of the article based on the given information about the selling prices and gains.

### Step 1: Define the Variables
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate Selling Price for 35% Gain
The selling price (SP) when the article is sold at a 35% gain can be calculated as:
\[ SP_1 = CP + 35\% \text{ of } CP = x + 0.35x = 1.35x \]

### Step 3: Calculate Selling Price for 45% Gain
If the man sold the article for Rs. 50 more, he would gain 45%. Therefore, the new selling price can be expressed as:
\[ SP_2 = CP + 45\% \text{ of } CP = x + 0.45x = 1.45x \]
According to the problem, \( SP_2 = SP_1 + 50 \):
\[ 1.45x = 1.35x + 50 \]

### Step 4: Solve for Cost Price (CP)
Now, we can solve for \( x \):
\[ 1.45x - 1.35x = 50 \]
\[ 0.10x = 50 \]
\[ x = \frac{50}{0.10} = 500 \]

### Step 5: Calculate Selling Price for 56% Gain
Now, we need to find the marked price (MP) if he wants a profit of 56%. The selling price for a 56% gain is:
\[ SP_3 = CP + 56\% \text{ of } CP = x + 0.56x = 1.56x \]
Substituting the value of \( x \):
\[ SP_3 = 1.56 \times 500 = 780 \]

### Step 6: Conclusion
Thus, the marked price of the article, if there is no discount offered, should be Rs. 780.