The cost of a house was Rs X lakhs in 2005. After 3 years, the house sold it for `25%` more than she paid it. But she has to pay a tax of `50%` of the gain. The tax amount she has to pay is.

Options

A. `(X)/(2)`
B. `(X)/(8)`
C. `(X)/(4)`
D. `(X)/(24)`

Answer

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

### Step 1: Determine the Cost Price (CP)
The cost of the house in 2005 is given as Rs. X lakhs.

### Step 2: Calculate the Selling Price (SP)
The house is sold for 25% more than the cost price.
- To find the selling price, we can use the formula:
\[ SP = CP + (25\% \text{ of } CP) \]
- Since \( CP = X \) lakhs, we can express this as:
\[ SP = X + 0.25X = 1.25X \text{ lakhs} \]

### Step 3: Calculate the Gain
The gain is the difference between the selling price and the cost price.
- The gain can be calculated as:
\[ \text{Gain} = SP - CP = 1.25X - X = 0.25X \text{ lakhs} \]

### Step 4: Calculate the Tax on the Gain
The problem states that a tax of 50% of the gain must be paid.
- The tax amount can be calculated as:
\[ \text{Tax} = 50\% \text{ of Gain} = 0.5 \times (0.25X) = 0.125X \text{ lakhs} \]

### Step 5: Convert the Tax Amount to a Fraction
To express the tax amount in a simpler form:
- We can write:
\[ \text{Tax} = \frac{0.125X}{1} = \frac{X}{8} \text{ lakhs} \]

### Final Answer
The tax amount she has to pay is \( \frac{X}{8} \) lakhs.

---