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 solve the problem, we need to find the selling price of the Indian factory after Mr. Mittal sold both factories at a profit. Let's break down the steps:

### Step 1: Define Variables
Let the cost price of the Indian factory be \( x \) crores and the cost price of the Malaysian factory be \( 72 - x \) crores (since the total cost is Rs. 72 crores).

### Step 2: Calculate Selling Prices
- The selling price of the Indian factory (SP_India) at 16% profit:
\[ SP_{India} = x + 0.16x = 1.16x \]

- The selling price of the Malaysian factory (SP_Malaysia) at 24% profit:
\[ SP_{Malaysia} = (72 - x) + 0.24(72 - x) = 1.24(72 - x) \]

### Step 3: Total Selling Price
The total selling price (SP_Total) is the sum of the selling prices of both factories:
\[ SP_{Total} = SP_{India} + SP_{Malaysia} = 1.16x + 1.24(72 - x) \]

### Step 4: Calculate Total Profit
According to the problem, Mr. Mittal gained a total profit of 19% on the total cost of Rs. 72 crores:
\[ \text{Total Profit} = 0.19 \times 72 = 13.68 \text{ crores} \]
Thus, the total selling price can also be expressed as:
\[ SP_{Total} = 72 + 13.68 = 85.68 \text{ crores} \]

### Step 5: Set Up the Equation
Now we can set up the equation:
\[ 1.16x + 1.24(72 - x) = 85.68 \]

### Step 6: Simplify the Equation
Expanding the equation:
\[ 1.16x + 1.24 \times 72 - 1.24x = 85.68 \]
Calculating \( 1.24 \times 72 \):
\[ 1.24 \times 72 = 89.28 \]
So the equation becomes:
\[ 1.16x - 1.24x + 89.28 = 85.68 \]
Combining like terms:
\[ -0.08x + 89.28 = 85.68 \]

### Step 7: Solve for \( x \)
Subtract 89.28 from both sides:
\[ -0.08x = 85.68 - 89.28 \]
\[ -0.08x = -3.6 \]
Dividing both sides by -0.08:
\[ x = \frac{-3.6}{-0.08} = 45 \text{ crores} \]

### Step 8: Find Selling Price of Indian Factory
Now, we can find the selling price of the Indian factory:
\[ SP_{India} = 1.16x = 1.16 \times 45 = 52.2 \text{ crores} \]

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

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