Alphonso, on his death bed, keeps half his property for this wife

Question

Alphonso, on his death bed, keeps half his property for this wife and divides 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, sharing 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.What was the worth of the total property?

A. Rs. 30 lakh
B. Rs. 8 lakh
C. Rs. 18 lakh
D. Rs. 24 lakh
E. Rs. 12 lakh

A. Rs. 30 lakh
B. Rs. 8 lakh
C. Rs. 18 lakh
D. Rs. 24 lakh
E. Rs. 12 lakh

CrackverbalGMAT · Answer

This can get a little complicated because of the fractions involved.

Let the total property value = x lakhs

When Alphonso dies: His wife's share =  \frac{x}{2} .

Each of the 3 brother gets 1/3 rd remaining  \frac{x}{2} = \frac{x}{6}

When Ben dies: His wife's share =  \frac{1}{2} * \frac{x}{6} = \frac{x}{12}

Dave and Carl each get 1/2 of the remaining  \frac{x}{12} = \frac{x}{24}

Now Dave and Carl each have  \frac{x}{6} + \frac{x}{24} = \frac{5x}{24}

When Carl dies: His wife's share =  \frac{1}{2} * \frac{5x}{24} = \frac{5x}{48}  and Dave gets the other half =  \frac{5x}{48}

Dave now has =  \frac{5x}{24} + \frac{5x}{48} = \frac{15x}{48} = \frac{5x}{16}

When Dave dies, his mother get 1/2 of his property =  \frac{1}{2} * \frac{5x}{16} = \frac{5x}{32}

The property share owned by the mother =  \frac{1}{2} + \frac{5x}{32} = \frac{21x}{32} = 1575000

x = \frac{1575000 * 32}{21} = 2400000

Option D

Arun Kumar

Abhishek009 · Answer

Let , Alphonsohad 300

He divided it as -

Wife = 150
Ben = 50
Carl = 50
Dave = 50

Ben's wife = 25
Carl = 50+12.5 = 62.50
Dave = 50+12.5 = 62.50

Carl's wife = 31.25
Dave = 62.50 + 31.25 = 93.75

Dave's wife = 46.875
Daves's Mother = 150 + 46.87 = 196.875

\frac{1575000}{196.875}*300 = 2400000 , Answer must be (D)

PS : Bit Lengthy for GMAT

bumpbot · Answer

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Alphonso, on his death bed, keeps half his property for this wife

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Alphonso, on his death bed, keeps half his property for this wife

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