When a person sold an article, his profit percent was ’ `60%` of the selling price. If the cost price is increased by `75%` and the selling price remains the same, then find that decrement in the profit is what per cent of the selling price of the article,

Options

A. `25%`
B. `30%`
C. `40%`
D. `27.5%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
- Profit percent = 60% of the selling price (SP)
- Let the selling price (SP) be \( x \).

### Step 2: Calculate the profit
- Profit (P) = 60% of SP
- Therefore, \( P = 0.6x \).

### Step 3: Calculate the cost price (CP)
- Cost Price (CP) can be calculated as:
\[ CP = SP - Profit = x - 0.6x = 0.4x \]

### Step 4: Increase the cost price by 75%
- New Cost Price (CP') after a 75% increase:
\[ CP' = CP + 0.75 \times CP = 0.4x + 0.75 \times 0.4x = 0.4x + 0.3x = 1.1x \]

### Step 5: Calculate the new profit
- Since the selling price remains the same, the new profit (P') is:
\[ P' = SP - CP' = x - 1.1x = -0.1x \]
(This indicates a loss, but we will consider the absolute value for profit decrement.)

### Step 6: Calculate the decrement in profit
- Original profit = \( 0.6x \)
- New profit = \( -0.1x \) (considering as a loss)
- Decrement in profit = Original profit - New profit
\[ \text{Decrement} = 0.6x - (-0.1x) = 0.6x + 0.1x = 0.7x \]

### Step 7: Calculate the percentage decrement in profit with respect to the selling price
- Percentage decrement in profit:
\[ \text{Percentage} = \left( \frac{\text{Decrement}}{\text{Selling Price}} \right) \times 100 = \left( \frac{0.7x}{x} \right) \times 100 = 70\% \]

### Final Answer
The decrement in profit is **70%** of the selling price of the article.

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