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. what was the worth of the total property in lacs?
Answers
( note: it is taken that Carl shares has been divided according to his will).
The worth of the total property is 24 lacs.
Given :
Amount left with mother at the end = Rs.1575000
To find :
The worth of the total property in lacs
Solution :
Let the worth of the total property be = x lakhs
After Alphonso's death :
His wife's share = x/2
Each of the 3 brother gets 1/3 rd of the remaining x/2 = 1/3 × x/2 = x/6
After Ben's death :
His wife's share = 1/2 × x/6 = x/12
Dave and Carl each get 1/2 of the remaining
= 1/2 × x/12
= x/24 each
Now Dave and Carl each have x/6 + x/12
=5x/24
After Carl death :
His wife's share = 1/2 × 5x/24
= 5x / 48
and Dave gets the other half = 5x/48
Dave now has = 5x/48 + 5x/24
= 15x/48
= 5x/16
After Dave's death,
his mother get 1/2 of his property = 5x/16 × 1/2
= 5x /32
The share of property owned by mother =
1/2 + 5x/32
= 21x/32
which is equal to 1575000
Hence x = (1575000 × 32)/21
= 2400000
Therefore, the total worth of property is 24lacs
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