The cost price of an article is C and the selling price of the same article is S, wehre Z is the profit or loss percentage. If the cost price and selling price both are increased by same amount then which of the following is true :

Options

A. Z increases
B. Z decreases
C. remains constant
D. none of these

Answer

To solve the problem step by step, we need to analyze the relationship between cost price (C), selling price (S), profit or loss percentage (Z), and how they change when both the cost price and selling price are increased by the same amount.

### Step 1: Understand the Definitions
- **Cost Price (C)**: The price at which an article is purchased.
- **Selling Price (S)**: The price at which an article is sold.
- **Profit (P)**: The difference between Selling Price and Cost Price, given by the formula:
\[ P = S - C \]
- **Profit Percentage (Z)**: The profit expressed as a percentage of the cost price, calculated using the formula:
\[ Z = \left(\frac{P}{C}\right) \times 100 \]

### Step 2: Analyze the Situation
If both the cost price and selling price are increased by the same amount, let’s denote this amount as \( x \). Therefore, the new cost price and selling price can be expressed as:
- New Cost Price: \( C' = C + x \)
- New Selling Price: \( S' = S + x \)

### Step 3: Calculate the New Profit
Using the new values, the new profit \( P' \) can be calculated as:
\[ P' = S' - C' = (S + x) - (C + x) = S - C = P \]
This shows that the actual profit remains the same after the increase.

### Step 4: Calculate the New Profit Percentage
Now, we need to find the new profit percentage \( Z' \):
\[ Z' = \left(\frac{P'}{C'}\right) \times 100 = \left(\frac{P}{C + x}\right) \times 100 \]
Since \( P \) remains constant, but \( C' \) (the new cost price) has increased, the denominator in the fraction has increased.

### Step 5: Analyze the Effect on Profit Percentage
As the cost price increases while the profit remains constant, the profit percentage \( Z' \) will decrease. This is because the profit is now a smaller fraction of a larger cost price.

### Conclusion
Thus, when both the cost price and selling price are increased by the same amount, the profit percentage \( Z \) decreases.

### Final Answer
The correct answer is: **Option 2: Z decreases.**

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