A man sells an article at a profit of 40%. If he had bought it at 40% less and sold for र 5 less,he would have gained 50%. Find the cost price of the article.

Options

A. र 10
B. र 15
C. र 20
D. र 30

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article based on the given conditions. Let's break it down:

### Step 1: Define the Selling Price with Initial Profit
Let the cost price of the article be \( CP \).

The man sells the article at a profit of 40%. Therefore, the selling price (SP1) can be calculated as:
\[ SP1 = CP + 40\% \text{ of } CP = CP + 0.4 \times CP = 1.4 \times CP \]
**Hint:** Remember that selling price can be calculated as cost price plus profit percentage of cost price.

### Step 2: Calculate the New Cost Price
If he had bought the article at 40% less, the new cost price (CP_new) would be:
\[ CP_{new} = CP - 40\% \text{ of } CP = CP - 0.4 \times CP = 0.6 \times CP \]
**Hint:** To find a price after a percentage reduction, subtract the percentage of the original price from the original price.

### Step 3: Define the New Selling Price
If he sells it for ₹5 less than the original selling price, the new selling price (SP2) can be expressed as:
\[ SP2 = SP1 - 5 = 1.4 \times CP - 5 \]
**Hint:** When a selling price is reduced by a fixed amount, subtract that amount from the original selling price.

### Step 4: Calculate the Selling Price with 50% Profit
According to the problem, if he sells at this new selling price, he would gain 50%. Thus, we can express SP2 in terms of CP_new:
\[ SP2 = CP_{new} + 50\% \text{ of } CP_{new} = CP_{new} + 0.5 \times CP_{new} = 1.5 \times CP_{new} \]
Substituting \( CP_{new} \):
\[ SP2 = 1.5 \times (0.6 \times CP) = 0.9 \times CP \]
**Hint:** To find selling price with a profit percentage, multiply the new cost price by \( 1 + \text{profit percentage} \).

### Step 5: Set the Two Expressions for SP2 Equal
Now we have two expressions for SP2:
1. \( SP2 = 1.4 \times CP - 5 \)
2. \( SP2 = 0.9 \times CP \)

Setting them equal gives us:
\[ 1.4 \times CP - 5 = 0.9 \times CP \]
**Hint:** When you have two expressions for the same quantity, you can set them equal to solve for the unknown.

### Step 6: Solve for CP
Rearranging the equation:
\[ 1.4 \times CP - 0.9 \times CP = 5 \]
\[ 0.5 \times CP = 5 \]
Now, divide both sides by 0.5:
\[ CP = \frac{5}{0.5} = 10 \]
**Hint:** To isolate the variable, perform the same operation on both sides of the equation.

### Conclusion
The cost price of the article is ₹10.

### Final Answer
The cost price of the article is **₹10**.