Comprehension
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his
three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and
half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his
property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some
years later, he keeps half his property for his widow and the remaining for his mother. The mother now
has Rs. 1,575,000.
Question: 1
What was the worth of the total property?
What was the worth of the total property?
Show Hint
Track what the mother (Alphonso’s wife) ends up with, as a fraction of the total property T, and equate it to Rs. 15.75 lakh.
Updated On: Nov 5, 2026
- Rs. 24 lakh
- Rs. 8 lakh
- Rs. 18 lakh
- Rs. 30 lakh
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Mother’s holding as a fraction of \(T\):
The mother (Alphonso’s wife) first has \(\frac{T}{2}\). Each son gets \(\frac{T}{6}\). Ben dies: Carl and Dave each get \(\frac{T}{24}\) more, so Carl and Dave each have \(\frac{5T}{24}\). Carl dies: Dave gets half of Carl’s \(\frac{5T}{24}\), that is \(\frac{5T}{48}\), so Dave has \(\frac{5T}{24}+\frac{5T}{48} = \frac{15T}{48} = \frac{5T}{16}\). Dave dies: the mother gets half of it, \(\frac{5T}{32}\).
Step 2: Equate to the given amount:
The mother now has \(\frac{T}{2}+\frac{5T}{32} = \frac{21T}{32} = 15{,}75{,}000\). So \(T = \frac{1575000\times 32}{21} = 24{,}00{,}000\), that is Rs. 24 lakh.
Step 3: Check with \(T = 24\) lakh:
Wife 12 lakh; each son 4 lakh. Ben dies: widow 2, Carl 5, Dave 5. Carl dies: widow 2.5, Dave 7.5. Dave dies: widow 3.75, mother gets 3.75. Mother: \(12+3.75 = 15.75\) lakh \(= 1{,}575{,}000\). Correct.
Final Answer:
The correct option is (1): Rs. 24 lakh.
The mother (Alphonso’s wife) first has \(\frac{T}{2}\). Each son gets \(\frac{T}{6}\). Ben dies: Carl and Dave each get \(\frac{T}{24}\) more, so Carl and Dave each have \(\frac{5T}{24}\). Carl dies: Dave gets half of Carl’s \(\frac{5T}{24}\), that is \(\frac{5T}{48}\), so Dave has \(\frac{5T}{24}+\frac{5T}{48} = \frac{15T}{48} = \frac{5T}{16}\). Dave dies: the mother gets half of it, \(\frac{5T}{32}\).
Step 2: Equate to the given amount:
The mother now has \(\frac{T}{2}+\frac{5T}{32} = \frac{21T}{32} = 15{,}75{,}000\). So \(T = \frac{1575000\times 32}{21} = 24{,}00{,}000\), that is Rs. 24 lakh.
Step 3: Check with \(T = 24\) lakh:
Wife 12 lakh; each son 4 lakh. Ben dies: widow 2, Carl 5, Dave 5. Carl dies: widow 2.5, Dave 7.5. Dave dies: widow 3.75, mother gets 3.75. Mother: \(12+3.75 = 15.75\) lakh \(= 1{,}575{,}000\). Correct.
Final Answer:
The correct option is (1): Rs. 24 lakh.
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Question: 2
What was Carl’s original share?
What was Carl’s original share?
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Carl’s original share is what he received from Alphonso’s will, before anything came to him from Ben. First find the total property.
Updated On: Nov 5, 2026
- Rs. 6 lakh
- Rs. 12 lakh
- Rs. 4 lakh
- Rs. 5 lakh
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Find the total property:
As worked out for the first question of this set, the mother ends up with \(\frac{T}{2}+\frac{5T}{32} = \frac{21T}{32} = 15{,}75{,}000\), so \(T = 24\) lakh.
Step 2: Carl’s original share:
Alphonso keeps half for his wife and divides the other half equally among three sons. Each son gets \(\frac{1}{3}\times\frac{T}{2} = \frac{T}{6} = \frac{24}{6} = 4\) lakh.
Step 3: Why not 5 lakh:
Carl later receives 1 lakh from Ben’s share, so he holds 5 lakh when he makes his will. That is his estate at the time of his death (option 4), not his original share. The word "original" refers to what he got at the first division.
Final Answer:
The correct option is (3): Rs. 4 lakh.
As worked out for the first question of this set, the mother ends up with \(\frac{T}{2}+\frac{5T}{32} = \frac{21T}{32} = 15{,}75{,}000\), so \(T = 24\) lakh.
Step 2: Carl’s original share:
Alphonso keeps half for his wife and divides the other half equally among three sons. Each son gets \(\frac{1}{3}\times\frac{T}{2} = \frac{T}{6} = \frac{24}{6} = 4\) lakh.
Step 3: Why not 5 lakh:
Carl later receives 1 lakh from Ben’s share, so he holds 5 lakh when he makes his will. That is his estate at the time of his death (option 4), not his original share. The word "original" refers to what he got at the first division.
Final Answer:
The correct option is (3): Rs. 4 lakh.
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Question: 3
What was the ratio of the property owned by the widows of the three sons, in the end?
What was the ratio of the property owned by the widows of the three sons, in the end?
Show Hint
Find how much each widow receives (half of each son’s holding at his death) and compare. The total property is Rs. 24 lakh.
Updated On: Nov 5, 2026
- 7 : 9 : 13
- 5 : 7 : 9
- 8 : 10 : 15
- 9 : 12 : 13
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Total property:
From the mother’s Rs. 15.75 lakh, \(T = 24\) lakh (as in the first question of this set).
Step 2: Each widow’s share:
Ben’s widow gets half of Ben’s 4 lakh \(= 2\) lakh. Carl holds \(4+1 = 5\) lakh when he dies, so his widow gets \(2.5\) lakh. Dave holds \(4+1+2.5 = 7.5\) lakh, so his widow gets \(3.75\) lakh.
Step 3: Ratio:
\(2 : 2.5 : 3.75 = 8 : 10 : 15\) (multiply by 4).
Final Answer:
The correct option is (3): 8 : 10 : 15.
From the mother’s Rs. 15.75 lakh, \(T = 24\) lakh (as in the first question of this set).
Step 2: Each widow’s share:
Ben’s widow gets half of Ben’s 4 lakh \(= 2\) lakh. Carl holds \(4+1 = 5\) lakh when he dies, so his widow gets \(2.5\) lakh. Dave holds \(4+1+2.5 = 7.5\) lakh, so his widow gets \(3.75\) lakh.
Step 3: Ratio:
\(2 : 2.5 : 3.75 = 8 : 10 : 15\) (multiply by 4).
Final Answer:
The correct option is (3): 8 : 10 : 15.
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