Mr. Mittal purchased two steel factories, one in India and other one in Malaysia for total rs 72 crores. Later on he sold the Indian factory at` 16%` profit and Malasian factory at `24%` profit. Thus he gained a total profit of `19%`. The selling price of Indian factory is :

Options

A. 45 crore
B. 52.2 crore
C. 8.55 crore
D. can not be determined

Answer

To find the selling price of the Indian factory, we can follow these steps:

### Step 1: Understand the Total Investment
Mr. Mittal purchased two factories for a total of Rs. 72 crores.

### Step 2: Set Up the Profit Percentages
- The Indian factory was sold at a profit of 16%.
- The Malaysian factory was sold at a profit of 24%.
- The total profit from both factories was 19%.

### Step 3: Use Alligation to Find the Ratio of Cost Prices
We can use the method of alligation to find the ratio of the cost prices of the two factories.

- Profit percentages:
- Indian factory: 16%
- Malaysian factory: 24%
- Total profit: 19%

Using alligation:
- The difference between the profit of the Malaysian factory and the total profit: \( 24\% - 19\% = 5\% \)
- The difference between the total profit and the profit of the Indian factory: \( 19\% - 16\% = 3\% \)

The ratio of the cost prices of the Indian factory to the Malaysian factory is:
\[ \text{Ratio} = 5 : 3 \]

### Step 4: Calculate the Cost Prices
Let the cost price of the Indian factory be \( 5x \) and the cost price of the Malaysian factory be \( 3x \).

According to the problem:
\[ 5x + 3x = 72 \text{ crores} \]
\[ 8x = 72 \text{ crores} \]
\[ x = 9 \text{ crores} \]

Now substituting back to find the cost prices:
- Cost price of the Indian factory:
\[ CP_{\text{Indian}} = 5x = 5 \times 9 = 45 \text{ crores} \]
- Cost price of the Malaysian factory:
\[ CP_{\text{Malaysian}} = 3x = 3 \times 9 = 27 \text{ crores} \]

### Step 5: Calculate the Selling Price of the Indian Factory
The selling price (SP) of the Indian factory can be calculated using the profit percentage:
\[ SP = CP + \text{Profit} \]
Profit from the Indian factory at 16%:
\[ \text{Profit} = 16\% \text{ of } 45 \text{ crores} = \frac{16}{100} \times 45 = 7.2 \text{ crores} \]
Thus, the selling price of the Indian factory is:
\[ SP_{\text{Indian}} = 45 + 7.2 = 52.2 \text{ crores} \]

### Final Answer
The selling price of the Indian factory is **Rs. 52.2 crores**.

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