Question

A man divides his property so that his son's share to his wife's and the wife's share to his daughter are both in the ratio \(3:1\). If the daughter gets 10,000 less than the son, find the total worth of the property.

Answer 1

Correct Answer: 4

Concept: This is a
ratio distribution problem:

• Combine ratios step-by-step
• Maintain consistency across relations

Step 1: Assign ratios.
\[ \text{Son : Wife} = 3 : 1 \] \[ \text{Wife : Daughter} = 3 : 1 \]
Step 2: Make ratios consistent.
Let wife = 3 units (common) \[ \text{Son : Wife} = 9 : 3 \] \[ \text{Wife : Daughter} = 3 : 1 \] Thus: \[ \text{Son : Wife : Daughter} = 9 : 3 : 1 \]
Step 3: Use given condition.
\[ \text{Difference (Son - Daughter)} = 9 - 1 = 8 \text{ units} \] \[ 8 \text{ units} = 10{,}000 \Rightarrow 1 \text{ unit} = 1250 \]
Step 4: Find total property.
\[ \text{Total units} = 9 + 3 + 1 = 13 \] \[ \text{Total} = 13 \times 1250 = 16{,}250 \]
Step 5: Option analysis.

• (A) 20,000: Incorrect $\times$
• (B) 16,000: Incorrect $\times$
• (C) 15,750: Incorrect $\times$
• (D) 16,250: Correct \checkmark
• (E) 20,500: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (D).