Mr. Ambani purchased two steel factories in Mumbai and Chennai for total Rs.72 crores. After a year, he sold Mumbai factory at 16% profit while other at 24% profit. Thus he gained 19% profit on selling both factories. Find the selling price of Mumbai factory? (in crores) Cannot be determined

Options

A. `52.2`
B. `55.8`
C. `53.55`
D. cannot be determined

Answer

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

### Step 1: Understand the total cost price of both factories
Mr. Ambani purchased two factories for a total of Rs. 72 crores.

### Step 2: Set up the profit percentages
- Mumbai factory is sold at a profit of 16%.
- Chennai factory is sold at a profit of 24%.
- The overall profit from selling both factories is 19%.

### Step 3: Calculate the profit ratios
We can set up the profit ratios based on the given percentages:
- Profit from Mumbai factory = 16%
- Profit from Chennai factory = 24%
- Overall profit = 19%

The difference in profit percentages can help us find the ratio of the cost prices of the two factories:
- Difference for Mumbai = 19% - 16% = 3%
- Difference for Chennai = 24% - 19% = 5%

Thus, the ratio of the cost prices of the Mumbai factory to the Chennai factory is 5:3.

### Step 4: Calculate the individual cost prices
Let the cost price of the Mumbai factory be 5x and the cost price of the Chennai factory be 3x. According to the problem:
\[ 5x + 3x = 72 \text{ crores} \]
\[ 8x = 72 \text{ crores} \]
\[ x = 9 \text{ crores} \]

Now, we can find the cost prices:
- Cost price of Mumbai factory = \( 5x = 5 \times 9 = 45 \text{ crores} \)
- Cost price of Chennai factory = \( 3x = 3 \times 9 = 27 \text{ crores} \)

### Step 5: Calculate the selling price of the Mumbai factory
To find the selling price, we need to add the profit to the cost price:
- Profit from Mumbai factory = 16% of 45 crores
\[ \text{Profit} = \frac{16}{100} \times 45 = 7.2 \text{ crores} \]

Now, calculate the selling price:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
\[ \text{Selling Price} = 45 + 7.2 = 52.2 \text{ crores} \]

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

---