# 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

Note by Rohitas Bansal
7 years, 6 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $\boxed{123}$

Sort by:

Most realistic values of their present ages are --

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

- 7 years, 6 months ago

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

- 7 years, 6 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 ?

- 7 years, 6 months ago

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

- 7 years, 6 months ago