A man distributes all his money among his three sons such that he gives 7,500 to his elder son, `3/10` part of his total money to his second son and third son get sum of money received by both first and second sons. what is the total money?

Options

A. 30000
B. 35000
C. 18750
D. 37500

Answer

To solve the problem step by step, let's denote the total amount of money the man has as \( T \).

### Step 1: Define the total money
Let the total money be \( T \).

### Step 2: Amount given to the elder son
The elder son receives \( 7500 \).

### Step 3: Amount given to the second son
The second son receives \( \frac{3}{10} \) of the total money:
\[ \text{Amount to second son} = \frac{3}{10} T \]

### Step 4: Amount given to the third son
The third son receives the sum of the amounts given to the first and second sons:
\[ \text{Amount to third son} = 7500 + \frac{3}{10} T \]

### Step 5: Set up the equation
Since the total amount of money distributed to all three sons must equal the total money \( T \), we can write the equation:
\[ 7500 + \frac{3}{10} T + \left( 7500 + \frac{3}{10} T \right) = T \]

### Step 6: Simplify the equation
Combine the terms:
\[ 7500 + \frac{3}{10} T + 7500 + \frac{3}{10} T = T \]
This simplifies to:
\[ 15000 + \frac{6}{10} T = T \]
or
\[ 15000 + \frac{3}{5} T = T \]

### Step 7: Isolate \( T \)
Subtract \( \frac{3}{5} T \) from both sides:
\[ 15000 = T - \frac{3}{5} T \]
This can be rewritten as:
\[ 15000 = \frac{2}{5} T \]

### Step 8: Solve for \( T \)
Multiply both sides by \( \frac{5}{2} \):
\[ T = 15000 \times \frac{5}{2} = 37500 \]

### Conclusion
The total amount of money the man has is \( T = 37500 \).

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