A father in his will left all his money to his children in the following manner: Rs. 1000 to the first born and l/io of what then remains, then Rs. 2000 to the second born and 1/10 of what then remains, then Rs. 3000 to the third born and 1/10 of what then remains, and so on. When this was done each child had the same amount. How many children did the father have?
Answers
Given : A father , in his will , left his money to his children in the following manner : 1000 to the first born and 1/10 of what then remains , then . 2000 to the second born and 1/10 of what then remains, then. 3000 to the third born and 1/10 of what then , remains. and so on .
each child had the same amount
To Find : how many children were there
Solution:
Let say Amount = Rs 100A
1000 to the first born and 1/10 of what then remains
= 1000 + (100A - 1000)/10
= 1000 + 10A - 100
= 900 + 10A
Amount left now = 100A - (900 + 10A)
= 90A - 900
2000 to the second born and 1/10 of what then remains,
= 2000 + ( 90A - 900 - 2000)/100
= 2000 + 9A - 290
= 1710 + 9A
900 + 10A = 1710 + 9A
=> A = 810
100A = 81000
1st got ( 1000 + (81000 - 1000)/10) = 9000
2nd got (2000 + (72000 - 2000)/10) = 9000
3rd got ( 3000 + (63000 - 3000)/10) = 9000
and son on
Last got = (9000 + (9000 - 9000)/10) = 9000
Number of children = 81000/9000 = 9
9 children , each got Rs 9000 & will amount = Rs 81000
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