The cost price of an article is C and the selling price of the same article is.S, where 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, we need to analyze the situation where both the cost price (C) and the selling price (S) of an article are increased by the same amount. We will derive the implications of this change on profit or loss percentage.

### Step-by-step Solution:

1. **Define the Initial Values**:
- Let the cost price be \( C \).
- Let the selling price be \( S \).
- The profit or loss can be calculated as:
\[ \text{Profit or Loss} = S - C \]

2. **Calculate Initial Profit or Loss Percentage**:
- If \( S > C \), we have a profit, and the profit percentage \( Z \) is given by:
\[ Z = \left( \frac{S - C}{C} \right) \times 100 \]
- If \( S < C \), we have a loss, and the loss percentage is:
\[ Z = \left( \frac{C - S}{C} \right) \times 100 \]

3. **Increase Both Prices by the Same Amount**:
- Let’s say both the cost price and selling price are increased by an amount \( x \).
- New cost price \( C' = C + x \)
- New selling price \( S' = S + x \)

4. **Calculate New Profit or Loss**:
- The new profit or loss becomes:
\[ \text{New Profit or Loss} = S' - C' = (S + x) - (C + x) = S - C \]
- This shows that the profit or loss remains the same.

5. **Calculate New Profit or Loss Percentage**:
- The new profit or loss percentage \( Z' \) is calculated as:
\[ Z' = \left( \frac{S' - C'}{C'} \right) \times 100 = \left( \frac{S - C}{C + x} \right) \times 100 \]
- Since \( C + x > C \), the denominator increases, which implies that \( Z' \) will be less than \( Z \) if there was a profit initially, and greater than \( Z \) if there was a loss initially.

6. **Conclusion**:
- Therefore, if both the cost price and the selling price are increased by the same amount, the profit percentage decreases if there was a profit initially, and the loss percentage increases if there was a loss initially.

### Final Answer:
The correct conclusion is that the profit percentage decreases or the loss percentage increases when both the cost price and selling price are increased by the same amount.