Ramesh sells an article at a loss of 5%. If he buys it for 30% less price and sells it for Rs. 38.5 less, then his profit will be 20%. What is the cost price (in Rs) of the article?

Options

A. 450
B. 300
C. 350
D. 250

Answer

To solve the problem step by step, let's denote the original cost price of the article as \( CP \).

### Step 1: Define the original cost price
Let the original cost price (CP) of the article be \( 100x \).

### Step 2: Calculate the selling price with a 5% loss
Since Ramesh sells the article at a loss of 5%, the selling price (SP) can be calculated as:
\[ SP = CP - (5\% \text{ of } CP) = 100x - 0.05 \times 100x = 95x \]

### Step 3: Calculate the new cost price after a 30% reduction
If Ramesh buys the article for 30% less, the new cost price becomes:
\[ New \, CP = CP - (30\% \text{ of } CP) = 100x - 0.30 \times 100x = 70x \]

### Step 4: Calculate the selling price with a 20% profit on the new cost price
If he sells the article for Rs. 38.5 less than the selling price that would give him a 20% profit, we first find the selling price for a 20% profit:
\[ SP_{profit} = New \, CP + (20\% \text{ of } New \, CP) = 70x + 0.20 \times 70x = 70x + 14x = 84x \]

### Step 5: Set up the equation for the selling price
According to the problem, the selling price with the new cost price is Rs. 38.5 less than the original selling price:
\[ SP = SP_{profit} - 38.5 \]
Substituting the values we have:
\[ 95x = 84x - 38.5 \]

### Step 6: Solve for \( x \)
Now, rearranging the equation:
\[ 95x - 84x = -38.5 \]
\[ 11x = 38.5 \]
\[ x = \frac{38.5}{11} = 3.5 \]

### Step 7: Calculate the original cost price
Now, substituting \( x \) back to find the original cost price:
\[ CP = 100x = 100 \times 3.5 = 350 \]

Thus, the original cost price of the article is **Rs. 350**.