Vinay sold a plot of land for Rs. 143000, gaining 4%. For how much did he purchase the plot?

Answer

To find out how much Vinay purchased the plot of land for, we can use the formula related to profit and loss. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 143,000
- Gain Percentage (GP) = 4%

### Step 2: Use the formula to find the Cost Price (CP)
The formula to find the Cost Price when the Selling Price and Gain Percentage are known is:

\[ CP = \frac{100}{100 + \text{Gain Percentage}} \times SP \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:

\[ CP = \frac{100}{100 + 4} \times 143000 \]

### Step 4: Simplify the equation
Now, simplify the equation:

\[ CP = \frac{100}{104} \times 143000 \]

### Step 5: Calculate the fraction
Now, we can simplify \(\frac{100}{104}\):

\[ \frac{100}{104} = \frac{25}{26} \]

### Step 6: Multiply by the Selling Price
Now, we multiply this fraction by the Selling Price:

\[ CP = \frac{25}{26} \times 143000 \]

### Step 7: Perform the multiplication
Now, calculate the multiplication:

\[ CP = 25 \times \frac{143000}{26} \]

Calculating \(\frac{143000}{26}\):

\[ \frac{143000}{26} = 5500 \]

Now, multiply by 25:

\[ CP = 25 \times 5500 = 137500 \]

### Step 8: Conclusion
Thus, the Cost Price (CP) of the plot is Rs. 137,500.

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