The cost of a house was X lakhs in 2005. After 3 years, the owner of 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.
एक मकान की लागत 2005 में 18 लाख थी। 3 वर्ष बाद मकान मालिक ने उसे भुगतान राशि 25% अधिक पर बेचा परन्तु उसे लाभ का 50% कर देना है। उसे कितनी कर राशि देनी होगी?

Options

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

Explanation

To solve the problem step by step, we will break down the calculations involved in determining the tax amount that the house owner has to pay.

### Step 1: Determine the cost price (CP) of the house
The cost of the house in 2005 is given as 18 lakhs.

**Hint:** Remember that the cost price is the initial amount paid for the house.

### Step 2: Calculate the selling price (SP) after 3 years
The owner sold the house for 25% more than the cost price.

To find the selling price:
- Calculate 25% of the cost price:
\[ \text{Gain} = 25\% \text{ of } 18 \text{ lakhs} = \frac{25}{100} \times 18 = 4.5 \text{ lakhs} \]
- Add this gain to the cost price to find the selling price:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Gain} = 18 + 4.5 = 22.5 \text{ lakhs} \]

**Hint:** When calculating percentages, convert the percentage to a fraction or decimal to simplify calculations.

### Step 3: Calculate the profit
The profit made from selling the house is the gain calculated in Step 2, which is 4.5 lakhs.

**Hint:** Profit is the difference between the selling price and the cost price.

### Step 4: Calculate the tax on the profit
The tax is 50% of the profit.

To find the tax amount:
\[ \text{Tax} = 50\% \text{ of Profit = } \frac{50}{100} \times 4.5 = 2.25 \text{ lakhs} \]

**Hint:** To find a percentage of a number, multiply the number by the percentage expressed as a decimal.

### Conclusion
The amount of tax the house owner has to pay is 2.25 lakhs.

**Final Answer:** 2.25 lakhs