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Akriti
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After six months, Seena will be 17 and Reena will be 28.

Or a more direct answer: Reena is 27 1/2 years old now.


(1) r+s=44

(2) r=2*s1

(3) r1=s2/2

(4) s2=3*r3

(5) r3=3*s3

-------

r>s (from (5))

Let t=r-s=r1-s1=r2-s2=r3-s3>0.

Then (6) t=2*s3 (from (5))

r= (from (2))

=2*(r1-t)= (from (3))

=2*(s2/2-t) = (from (4))

=3*r3-2*t = 

=3*s3+3*t-2*t = (from (6))

=3*t/2+t=5/2*t

s=r-t= 5/2*t-t=3*t/2

44=r+s=5/2*t+3*t/2=4*t

Therefore t=11, s=(44-11)/2=16.5, r = s+t = 27.5

Edited by araver
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Hmmmmmm....I am totally confused!! :wacko:

:thanks: great job ,but actually I couldn't understand it.

Sorry, I was in a hurry :)

Let r=age of Reena now and s = age of Seena now. Then from the first statement we get:


(1) r+s=44

Reading further: "...Reena is twice as old as Seena was ..." sometime ago - let's call it Time 1. Let s1 and r1 be the ages of Seena and Reena in time 1. Then this statement means:

(2) r=2*s1

Reading further: "... as seena was when reena was half as old as seena will be when ... " - sometime in the future - let's call it Time 2. Let s2 and r2 be the ages of Seena and Reena in time 2. Then this statement means:

(3) r1=s2/2

Reading further: "...when seena is three times as old as reena was... " sometime ago - Time 3. Let s2 and r2 be the ages of Seena and Reena in time 3. Then this statement means:

(4) s2=3*r3

Reading further: "...when reena was three times as old as seena. " still in Time 3, so:

(5) r3=3*s3

From (5) we get that Reena is older than Seena. But the age difference between Reena and Seena is constant so:
 Let t=r-s=r1-s1=r2-s2=r3-s3>0 
Then replacing r3 in (5) we get:
(6) t=2*s3
And now we use all these relations backwards to see how old is Reena now (in terms of t). Each time a previous statement is used it is marked.

r= (from (2))  = 2*(r1-t)

 = (from (3))  = 2*(s2/2-t) 

 = (from (4))  = 3*r3-2*t  

 = (def. of t) = 3*s3+3*t-2*t 

 = (from (6))  = 3*t/2+t

 = 5*t/2

Then

s = r-t = 5/2*t - t= 3*t/2

Replacing in (1):

44 = r+s = 5*t/2 + 3*t/2 =4*t

Therefore
 t=11, s=(44-11)/2=16.5, r = s+t = 27.5

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