document.write( "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.
\n" ); document.write( "‘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’
\n" ); document.write( "‘That is very well, Sunanya’ said the teacher, but what I asked is not the age of your sister Nithya but your own age’.
\n" ); document.write( "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?
\n" ); document.write( "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.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #476896 by ankor@dixie-net.com(22740)\"\" \"About 
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’
\n" ); document.write( "Let s = Sunny's age
\n" ); document.write( "Let n = Nithya' age
\n" ); document.write( "Let m = Mom's age
\n" ); document.write( "Let f = Dad's age
\n" ); document.write( ":
\n" ); document.write( "When I was born:
\n" ); document.write( "my only sister Nithya , happened to be just one quarter the age of my mother
\n" ); document.write( "n - s = .25(m - s)
\n" ); document.write( "n - s = .25m - .25s
\n" ); document.write( "n = .25m - .25s + s
\n" ); document.write( "n = .25m + .75s
\n" ); document.write( "and she is now one third the age of our father’
\n" ); document.write( "n = .33f
\n" ); document.write( "n = n, therefore
\n" ); document.write( ".33f = .25m + .75s
\n" ); document.write( "I am just a quarter of my mother’s present age
\n" ); document.write( "s = .25m
\n" ); document.write( "Replace .25m with s
\n" ); document.write( ".33f = s + .75s
\n" ); document.write( ".33f = 1.75s
\n" ); document.write( "Multiply both sides by 3
\n" ); document.write( "f = 5.25s
\n" ); document.write( " and in four years time I shall be a quarter the age of my father.
\n" ); document.write( "(s+4) = .25(f+4)
\n" ); document.write( "s + 4 = .25f + 1
\n" ); document.write( "s = .25f + 1 - 4
\n" ); document.write( "s = .25f - 3
\n" ); document.write( "replace f with 5.25s
\n" ); document.write( "s = .25(5.25s) - 3
\n" ); document.write( "s = 1.3125s - 3
\n" ); document.write( "3 = 1.3125s - s
\n" ); document.write( "3 = .3125s
\n" ); document.write( "s = 3/.3125
\n" ); document.write( "s = 9.6 yrs is Sunny's present age
\n" ); document.write( ";
\n" ); document.write( "I was expecting an integer solution (hoping!) but this seems to check out
\n" ); document.write( "I got
\n" ); document.write( "n = 16.8
\n" ); document.write( "m = 38.4
\n" ); document.write( "f = 50.4\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );