When Maharaja Ram
Singh died in 1825, he left 3465
gold pieces to be divided
equally among his children.
Each wife had the same
number of children which was
8 less than the number of
wives per harem. Number of
wives per harem was 4 more
than the number of harems.
Number of children per wife is
12 less than the number of
gold pieces each of them
received. How many children
did Ram Singh have?
Answers
Given : 3465 gold pieces to be divided equally among his children.
Each wife had the same number of children which was 8 less than the number of wives per harem.
Number of wives per harem was 4 more than the number of harems.
Number of children per wife is 12 less than the number of gold pieces each of them received.
To Find : How many children did Ram Singh have?
Solution:
Gold pieces = 3465
Harem = H
Number of wives per harem was 4 more than the number of harems.
Wives per harem H + 4
Total number of wives = H ( H + 4)
Each wife had the same number of children which was 8 less than the number of wives per harem.
Children for each wife = H + 4 - 8 = H - 4
Total Children = H(H + 4)(H - 4)
Number of children per wife ( H - 4) is 12 less than the number of gold pieces each of them received.
Hence number of gold pieces each of them received. = H - 4 + 12 = H + 8
H(H + 4)(H - 4) ( H + 8) = 3465
3465 = 3 * 3 * 5 * 7 * 11 = 3 * 7 * 11 * 15
(H - 4)(H )(H + 4)(H + 8)
( 7 - 4)(7) ( 7 + 4)(7 + 8)
H = 7
Total Children = H(H + 4)(H - 4)
= 7 ( 7 + 4)(7 - 4)
= 231
Gold piece each received = 3465 / 231 = 15
Lets verify each thing :
Harem = H = 7
Wives per harem = 7 + 4 = 11 => Total Wives = 7 * 11 = 77
Children for each wife = 11 - 8 = 3 => total children = 77 * 3 = 231
Gold piece each received = 3465 / 231 = 15
Number of children per wife is 12 less than the number of gold pieces each of them received. = 15 - 12 = 3 ( satisfied)
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