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 need to determine the cost price of the article and then find the marked price for a desired profit of 56%.

### Step 1: Understand the given information
- The man sells the article at a 35% gain.
- If he sells it for Rs. 50 more, he gains 45%.

### Step 2: Let the cost price (CP) of the article be \( x \).
- Selling Price (SP) at 35% gain:
\[ SP_1 = CP + 35\% \text{ of } CP = x + 0.35x = 1.35x \]

### Step 3: Calculate the selling price at 45% gain.
- Selling Price (SP) at 45% gain:
\[ SP_2 = CP + 45\% \text{ of } CP = x + 0.45x = 1.45x \]

### Step 4: Set up the equation based on the information given.
- According to the problem:
\[ SP_2 = SP_1 + 50 \]
Substituting the values we found:
\[ 1.45x = 1.35x + 50 \]

### Step 5: Solve for \( x \).
- Rearranging the equation:
\[ 1.45x - 1.35x = 50 \]
\[ 0.10x = 50 \]
\[ x = \frac{50}{0.10} = 500 \]
- So, the cost price of the article is Rs. 500.

### Step 6: Calculate the selling price for a 56% gain.
- Selling Price (SP) for a 56% gain:
\[ SP = CP + 56\% \text{ of } CP = x + 0.56x = 1.56x \]
Substituting \( x = 500 \):
\[ SP = 1.56 \times 500 = 780 \]

### Step 7: Conclusion
- The marked price of the article, if no discount is offered, should be Rs. 780.