A man sells an article at 10% loss. If he buys it at 20% less its C.P. and sells it for Rs 55 more than the first S.P., he gain 40%. Find the C.P.

Options

A. Rs 110
B. Rs 121
C. Rs 120
D. Rs 250

Answer

To solve the problem step by step, we will define the variables and use the information given in the question to find the Cost Price (C.P.) of the article.

### Step 1: Define the variables
Let the original Cost Price (C.P.) of the article be \( C \).

### Step 2: Calculate the Selling Price (S.P.) at 10% loss
Since the man sells the article at a 10% loss, the Selling Price (S.P.) can be calculated as:
\[ \text{S.P.} = C - 0.1C = 0.9C \]

### Step 3: Calculate the new Cost Price
The man buys the article at 20% less than its original C.P. Therefore, the new C.P. is:
\[ \text{New C.P.} = C - 0.2C = 0.8C \]

### Step 4: Calculate the new Selling Price
The new Selling Price is Rs. 55 more than the first S.P. Therefore, we can express the new S.P. as:
\[ \text{New S.P.} = 0.9C + 55 \]

### Step 5: Set up the equation for profit
The profit made on selling the article at the new S.P. is given as 40%. The profit can be calculated using the formula:
\[ \text{Profit} = \text{New S.P.} - \text{New C.P.} \]
Substituting the values we have:
\[ \text{Profit} = (0.9C + 55) - 0.8C = 0.1C + 55 \]

### Step 6: Set up the profit percentage equation
The profit percentage is given as 40%. Therefore, we can set up the equation:
\[ \frac{\text{Profit}}{\text{New C.P.}} \times 100 = 40 \]
Substituting the values we have:
\[ \frac{0.1C + 55}{0.8C} \times 100 = 40 \]

### Step 7: Simplify the equation
Now, let's simplify the equation:
\[ 0.1C + 55 = 0.4 \times 0.8C \]
\[ 0.1C + 55 = 0.32C \]

### Step 8: Rearranging the equation
Rearranging gives:
\[ 55 = 0.32C - 0.1C \]
\[ 55 = 0.22C \]

### Step 9: Solve for C
Now, solving for \( C \):
\[ C = \frac{55}{0.22} = 250 \]

### Conclusion
Thus, the original Cost Price (C.P.) of the article is:
\[ \boxed{250} \]