Question 783331: Sunny was recently sent to a new school in Peach City-Atlanta-GA.. On the first day of her arrival the teacher asked her age and this was Sunny’s curious reply.
‘Well, Madam, you see it is like this. At the time I was born, I forgot the year, my only sister Nithya , happened to be just one quarter the age of my mother and she is now one third the age of our father’
‘That is very well, Sunanya’ said the teacher, but what I asked is not the age of your sister Nithya but your own age’.
Sunanya then replied ‘ Madam, I was just coming to that” and continued ‘ I am just a quarter of my mother’s present age and in four years time I shall be a quarter the age of my father. Is not that funny?
This was all the information that the teacher could get from Sunanaya. Could you work out, from the facts what was Sunanaya’s age? It is certainly little puzzling.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! At the time I was born, I forgot the year, my only sister Nithya , happened to be just one quarter the age of my mother and she is now one third the age of our father’
Let s = Sunny's age
Let n = Nithya' age
Let m = Mom's age
Let f = Dad's age
:
When I was born:
my only sister Nithya , happened to be just one quarter the age of my mother
n - s = .25(m - s)
n - s = .25m - .25s
n = .25m - .25s + s
n = .25m + .75s
and she is now one third the age of our father’
n = .33f
n = n, therefore
.33f = .25m + .75s
I am just a quarter of my mother’s present age
s = .25m
Replace .25m with s
.33f = s + .75s
.33f = 1.75s
Multiply both sides by 3
f = 5.25s
and in four years time I shall be a quarter the age of my father.
(s+4) = .25(f+4)
s + 4 = .25f + 1
s = .25f + 1 - 4
s = .25f - 3
replace f with 5.25s
s = .25(5.25s) - 3
s = 1.3125s - 3
3 = 1.3125s - s
3 = .3125s
s = 3/.3125
s = 9.6 yrs is Sunny's present age
;
I was expecting an integer solution (hoping!) but this seems to check out
I got
n = 16.8
m = 38.4
f = 50.4
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