If a man were to sell his hand-cart for Rs 720, he would lose 25% . What must he sell it for to gain 25%?

Answer

To solve the problem step by step, we need to find the cost price of the hand-cart first, and then determine the selling price needed to achieve a 25% gain.

### Step 1: Understand the Loss
Given that selling the hand-cart for Rs 720 results in a loss of 25%, we can use this information to find the cost price (CP).

### Step 2: Calculate the Cost Price (CP)
The formula to calculate the cost price when there is a loss is:
\[ CP = \frac{SP}{(1 - \frac{Loss \%}{100})} \]
Where:
- SP = Selling Price
- Loss % = 25%

Substituting the values:
\[ CP = \frac{720}{(1 - \frac{25}{100})} = \frac{720}{(1 - 0.25)} = \frac{720}{0.75} \]

### Step 3: Simplify the Calculation
Now, we simplify the expression:
\[ CP = \frac{720}{0.75} = 720 \times \frac{100}{75} = 720 \times \frac{4}{3} = 960 \]

### Step 4: Calculate the Selling Price for a 25% Gain
Now that we have the cost price (CP = Rs 960), we can find the selling price (SP) required to achieve a 25% gain.

The formula to calculate the selling price when there is a gain is:
\[ SP = CP \times (1 + \frac{Gain \%}{100}) \]
Where:
- Gain % = 25%

Substituting the values:
\[ SP = 960 \times (1 + \frac{25}{100}) = 960 \times (1 + 0.25) = 960 \times 1.25 \]

### Step 5: Simplify the Selling Price Calculation
Now, we simplify the expression:
\[ SP = 960 \times 1.25 = 1200 \]

### Final Answer
The man must sell his hand-cart for Rs 1200 to gain 25%.

---