A person gave `Rs. 2500` to his eldest son, `5/12` of the whole property to the second son and to the youngest as much as to the first and the second son together. How much did the youngest son get?

Options

A. Rs. 10000
B. Rs. 15000
C. Rs. 20000
D. Rs. 25000

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variables
Let:
- A = amount received by the eldest son = Rs. 2500
- B = amount received by the second son
- C = amount received by the youngest son

### Step 2: Understand the distribution
According to the problem:
- The eldest son (A) received Rs. 2500.
- The second son (B) received \( \frac{5}{12} \) of the total property.
- The youngest son (C) received as much as the first and second sons together, which means \( C = A + B \).

### Step 3: Express the total property
Let the total property be denoted as \( P \). Therefore, we can express B as:
\[ B = \frac{5}{12} P \]

### Step 4: Express C in terms of A and B
Since C received as much as A and B together:
\[ C = A + B = 2500 + B \]

### Step 5: Express the total property in terms of C
Now we can express the total property in terms of C:
\[ P = A + B + C = A + B + (A + B) = 2(A + B) \]
Substituting \( B \):
\[ P = 2\left(2500 + B\right) \]

### Step 6: Substitute B in the total property equation
Now we can substitute \( B \) from step 3 into the total property equation:
\[ P = 2\left(2500 + \frac{5}{12} P\right) \]

### Step 7: Solve for P
Expanding the equation:
\[ P = 5000 + \frac{5}{6} P \]
Now, rearranging the equation:
\[ P - \frac{5}{6} P = 5000 \]
This simplifies to:
\[ \frac{1}{6} P = 5000 \]
Multiplying both sides by 6:
\[ P = 30000 \]

### Step 8: Calculate B
Now that we have the total property \( P \), we can find B:
\[ B = \frac{5}{12} P = \frac{5}{12} \times 30000 = 12500 \]

### Step 9: Calculate C
Now we can find C:
\[ C = A + B = 2500 + 12500 = 15000 \]

### Conclusion
Thus, the youngest son received Rs. 15000.

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