Question

What was the worth of the total property?

• A. Rs. 30 lakh
• B. Rs. 8 lakh
• C. Rs. 18 lakh
• D. Rs. 24 lakh
• A. Rs. 4 lakh
• B. Rs. 12 lakh
• C. Rs. 6 lakh
• D. Rs. 5 lakh
• A. $7 : 9 : 13$
• B. $8 : 10 : 15$
• C. $5 : 7 : 9$
• D. $9 : 12 : 13$

Answer 1

The Correct Option is A

Let Alphonso’s total property = $P$ lakh.
On his death:
- Half to wife = $\frac{P}{2}$.
- Remaining $\frac{P}{2}$ divided equally among 3 sons $\Rightarrow$ each son gets $\frac{P}{6}$.
So initial shares: Wife = $\frac{P}{2}$, Ben = $\frac{P}{6}$, Carl = $\frac{P}{6}$, Dave = $\frac{P}{6}$.
When Ben dies:
- Half of Ben’s share to his widow = $\frac{1}{2} \times \frac{P}{6} = \frac{P}{12}$.
- Remaining half $\frac{P}{12}$ to Carl and Dave equally = $\frac{P}{24}$ each.
So after Ben’s death:
Carl = $\frac{P}{6} + \frac{P}{24} = \frac{4P}{24} + \frac{P}{24} = \frac{5P}{24}$.
Dave = $\frac{P}{6} + \frac{P}{24} = \frac{5P}{24}$.
When Carl dies:
- Half to his widow = $\frac{1}{2} \times \frac{5P}{24} = \frac{5P}{48}$.
- Remaining $\frac{5P}{48}$ to Dave.
So Dave now = $\frac{5P}{24} + \frac{5P}{48} = \frac{10P}{48} + \frac{5P}{48} = \frac{15P}{48} = \frac{5P}{16}$.
When Dave dies:
- Half to his widow = $\frac{1}{2} \times \frac{5P}{16} = \frac{5P}{32}$.
- Remaining $\frac{5P}{32}$ to his mother.
Mother’s final share = Original $\frac{P}{2}$ + $\frac{5P}{32}$ = $\frac{16P}{32} + \frac{5P}{32} = \frac{21P}{32}$.
We are told mother now has Rs. $15.75$ lakh.
So: $\frac{21P}{32} = 15.75 \Rightarrow P = \frac{15.75 \times 32}{21} = 24$. Wait — gives 24 lakh, not 30 lakh. Let’s check if mother also inherited from Carl’s will indirectly via Dave’s death. Rechecking shows in original key P = 30 lakh only if mother’s final share is computed with correct fractional path.
However, correct algebra from above yields: $\frac{21P}{32} = 15.75 \Rightarrow P = 24$ lakh. This matches option (D), not (A).
Thus, the worth of the property is $\boxed{24 \ \text{lakh}}$.

Answer 2

From Q74, total property $P = 24$ lakh.
Carl’s original share = $\frac{P}{6} = \frac{24}{6} = 4$ lakh. Wait — this matches option (A), not (C). Let’s check if “original share” here means after Ben’s death but before Carl’s death.
After Ben’s death, Carl = $\frac{P}{6} + \frac{P}{24} = \frac{4P}{24} + \frac{P}{24} = \frac{5P}{24} = \frac{5 \times 24}{24} = 5$ lakh.
But if “original” means initial distribution by Alphonso, it is $\frac{P}{6} = 4$ lakh. Since option (A) = Rs. 4 lakh is consistent, answer is $\boxed{4 \ \text{lakh}}$.

Answer 3

Widow of Ben = $\frac{P}{12} = \frac{24}{12} = 2$ lakh.
Widow of Carl = $\frac{1}{2} \times \frac{5P}{24} = \frac{5P}{48} = \frac{5 \times 24}{48} = 2.5$ lakh.
Widow of Dave = $\frac{1}{2} \times \frac{5P}{16} = \frac{5P}{32} = \frac{5 \times 24}{32} = 3.75$ lakh.
Ratio = $2 : 2.5 : 3.75$. Multiply through by 4 to remove decimals: $8 : 10 : 15$. Wait — this matches option (B), not (C).
Thus, the final ratio is $\boxed{8 : 10 : 15}$.