Olympiad Problem ........ Mind Shaking or Boggling one !

The following relationship hold among the ages of the ages of the members of a family of four. All ages are integers.

The mother is three times as old as the daughter was when the father was the same age as the mother is now. When the daughter reaches half the age the mother is now, the son will be half as old as the father was when the mother was twice the age the daughter is now. When the father reaches twice the age the mother was when the daughter was the same age as the son is now, the daughter will be four times as old as the son is now. Given that one of their ages is a perfect square, what are the four ages ?

Please , In discussion write all the ages and how you arrived at them

#Algebra #NumberTheory #MathProblem #Internationalmathematicalolympiad #InternationalMathOlympiad(IMO)

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

Most realistic values of their present ages are --

Mother- 42 yrs Father- 44 yrs Daughter- 16 yrs Son- 12 yrs

Upendra Singh - 7 years, 5 months ago

Well done Upendra These are right but can u explain how did u get them

Rohitas Bansal - 7 years, 5 months ago

Actually I didn't post the entire solution because I thought it would ruin the pleasure of solving the problem for others who read this post ! :-) :-)

Still I can post it if you want...What say ?

Upendra Singh - 7 years, 5 months ago

No , u have kind thoughts........ and i have also solved it myself XD ....... so don't need the solution

Rohitas Bansal - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$