Mehul sold an item for ₹5,625 and incurred a loss of 25%. At what price should he have sold the item to gain a profit of25%?

Options

A. ₹9,375
B. ₹10,500
C. ₹8,250
D. Cannot be determined

Explanation

To solve the problem step by step, we will first determine the Cost Price (CP) of the item based on the Selling Price (SP) and the loss percentage. Then, we will calculate the Selling Price required to achieve a profit of 25%.

### Step 1: Determine the Cost Price (CP)
Given:
- Selling Price (SP) = ₹5,625
- Loss Percentage = 25%

Since there is a loss of 25%, the Selling Price represents 75% of the Cost Price (CP).

We can express this mathematically as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the values:
\[ 5625 = CP \times \left(1 - \frac{25}{100}\right) \]
\[ 5625 = CP \times 0.75 \]

To find CP, we rearrange the equation:
\[ CP = \frac{5625}{0.75} \]

Calculating CP:
\[ CP = \frac{5625 \times 100}{75} = \frac{562500}{75} = 7500 \]

### Step 2: Calculate the Selling Price for a Profit of 25%
Now that we have the Cost Price (CP), we need to find the Selling Price (SP) that would yield a profit of 25%.

The formula for Selling Price when there is a profit is:
\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
Substituting the values:
\[ SP = 7500 \times \left(1 + \frac{25}{100}\right) \]
\[ SP = 7500 \times 1.25 \]

Calculating the Selling Price:
\[ SP = 7500 \times 1.25 = 9375 \]

### Final Answer
Mehul should have sold the item for **₹9,375** to gain a profit of 25%.

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