`10%` of Brazil's population migrated to South Affrica `10%` of the remaining migrated to America and `10%` of rest migrated to Australia. If the female population which was left in Brazil remained only `3,64,500` , Find the population of Brazil city before the migration the female population was half the male population and this ratio did not change after the migration ?

Options

A. `1800000`
B. `1500000`
C. `1600000`
D. `1400000`

Answer

To solve the question step by step, we will break down the information given and perform calculations accordingly.

### Step 1: Understand the Migration Process
Initially, we know that 10% of Brazil's population migrated to South Africa, then 10% of the remaining population migrated to America, and finally, 10% of the remaining population migrated to Australia.

### Step 2: Set Up the Initial Population
Let the initial population of Brazil be \( P \).

### Step 3: Calculate the Population After Each Migration
1. **After migration to South Africa:**
- 10% of \( P \) migrated, so \( 0.1P \) left.
- Remaining population = \( P - 0.1P = 0.9P \).

2. **After migration to America:**
- 10% of the remaining \( 0.9P \) migrated, which is \( 0.1 \times 0.9P = 0.09P \).
- Remaining population = \( 0.9P - 0.09P = 0.81P \).

3. **After migration to Australia:**
- 10% of the remaining \( 0.81P \) migrated, which is \( 0.1 \times 0.81P = 0.081P \).
- Remaining population = \( 0.81P - 0.081P = 0.729P \).

### Step 4: Set Up the Equation for Remaining Female Population
According to the problem, the remaining female population in Brazil is \( 364,500 \). Therefore, we can set up the equation:
\[ 0.729P = 364,500 \]

### Step 5: Solve for \( P \)
To find \( P \), we rearrange the equation:
\[ P = \frac{364,500}{0.729} \]
Calculating this gives:
\[ P = 500,000 \]

### Step 6: Determine the Female and Male Population
From the problem, we know that the female population was half of the male population. Let the female population be \( F \) and the male population be \( M \). Thus:
\[ F = \frac{M}{2} \]
Since the total population \( P = F + M \), we can express \( M \) in terms of \( F \):
\[ P = F + 2F = 3F \]
So, we have:
\[ F = \frac{P}{3} = \frac{500,000}{3} \approx 166,667 \]
And:
\[ M = 2F = 2 \times 166,667 \approx 333,334 \]

### Step 7: Final Calculation of Total Population
The total population before migration was:
\[ P = F + M = 166,667 + 333,334 = 500,000 \]

### Conclusion
The total population of Brazil before migration was \( 500,000 \).

---