On selling a chair for Rs.720, a man loses 25%. To gain 25% it must be sold for

Options

A. Rs.900
B. Rs.1200
C. Rs.1080
D. Rs.1440

Answer

To solve the problem step by step, we need to determine the cost price (CP) of the chair first and then find the selling price (SP) required to achieve a 25% gain.

### Step 1: Identify the given values
- Selling Price (SP) when there is a loss = Rs. 720
- Loss Percentage = 25%

### Step 2: Use the formula to find the Cost Price (CP)
The formula for selling price when there is a loss is:
\[ SP = \left( \frac{100 - \text{Loss Percentage}}{100} \right) \times CP \]
Substituting the known values:
\[ 720 = \left( \frac{100 - 25}{100} \right) \times CP \]
This simplifies to:
\[ 720 = \left( \frac{75}{100} \right) \times CP \]

### Step 3: Rearranging the formula to find CP
To find CP, we can rearrange the equation:
\[ CP = 720 \times \left( \frac{100}{75} \right) \]

### Step 4: Calculate CP
Now, calculate CP:
\[ CP = 720 \times \frac{100}{75} = 720 \times \frac{4}{3} = 960 \]
So, the Cost Price (CP) of the chair is Rs. 960.

### Step 5: Calculate the Selling Price (SP) for a 25% gain
Now, we need to find the selling price that would give a 25% gain. The formula for selling price when there is a gain is:
\[ SP = \left( \frac{100 + \text{Gain Percentage}}{100} \right) \times CP \]
Substituting the values:
\[ SP = \left( \frac{100 + 25}{100} \right) \times 960 \]
This simplifies to:
\[ SP = \left( \frac{125}{100} \right) \times 960 \]

### Step 6: Calculate the new SP
Now calculate the new SP:
\[ SP = 1.25 \times 960 = 1200 \]
Thus, the selling price to gain 25% is Rs. 1200.

### Final Answer
To gain 25%, the chair must be sold for Rs. 1200.

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