By selling an article for 285 a man loses 5%. For how much should he sell to gain 5%?

Options

A. 315
B. 308
C. 305
D. none of these

Answer

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

### Step 1: Understand the given information
We know that selling an article for 285 results in a loss of 5%. This means that the selling price (SP) is 285 and the loss percentage is 5%.

### Step 2: Determine the cost price (CP)
If there is a 5% loss, it means the selling price is 95% of the cost price. We can express this mathematically as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the values we have:
\[ 285 = CP \times 0.95 \]
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{285}{0.95} \]

### Step 3: Calculate the cost price
Now, we can calculate the cost price:
\[ CP = \frac{285}{0.95} = 300 \]

### Step 4: Determine the selling price for a 5% gain
To find the selling price that would result in a 5% gain, we use the formula:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
Substituting the cost price and gain percentage:
\[ SP = 300 \times \left(1 + \frac{5}{100}\right) \]
\[ SP = 300 \times 1.05 \]

### Step 5: Calculate the selling price for a 5% gain
Now, we can calculate the selling price:
\[ SP = 300 \times 1.05 = 315 \]

### Conclusion
To gain 5%, the man should sell the article for **315**.

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