Question 983101: 1)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?.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! 1)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 THEN be just one quarter the age of my
mother AT PRESENT 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?.
That will only work if you insert the words AT PRESENT above.
Otherwise the ages come out as fractions.
1)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.
Suppose Sunny is S years old
‘Well, Madam, you see it is like this. At the time I was born, I forgot the year,
That was S years ago.
my only sister Nithya ,
Let Nithya's present age be N, so her age when Sonny was born was N-S
happened to be just one quarter the age of my mother AT PRESENT
Let the mother's age AT PRESENT be M
so N-S =  M
and she is now one third the age of our father’
Let the father's age be F
So N =  F
‘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.
So S = M
and in four years time I shall be a quarter the age of my father.
So S+4 = (F+4}}}
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?.
We have the system of equations
(1) N-S = M
(2) N = F
(3) S = M
(4) S+4 = (F+4)
Solve (4) for F
(4) S+4 = (F+4)
4(S+4) = F+4
4S+16 = F+4
(5) 4S+12 = F
Substitute in (2)
(2) N = F
3N = F
3N = 4S+12
(6) N = (4S+12)/3
Solve (3) for M
(3) S = M
(7) 4S = M
Use (6) and (7) to substitute for N and M in (1)
(1) N-S = M
4N-4S = M
4(4S+12)/3 - 4S = 4S
4(4S+12) - 12S = 12S
16S+48 - 12S = 12S
4S + 48 = 12S
48 = 8S
(8) 6 = S
We could quit there, for Sunny is 6. But we'll get the other ages.
Use (7) to get M
(7) 4S = M
4(6) = M
24 = M
Use (8) in (5) to get F
(5) 4(6)+12 = F
24+12 = F
(9) 36 = F
Use (9) in (2) to get N
(2) N = F
N = (36)
N = 12
Edwin
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