Age Puzzles: Explanation, Examples & Answers

Answer: My current age is 28 years and yours is 21 years

Explanation:

To solve this puzzle, you need to think about 3 different timelines, the past, now, and the future, and form equations based on these timelines as follows:

Let:

• P: My age in the past.
• P’: Your age in the past.
• N: My age now (current age).
• N’: Your age now (current age).
• F: My age in the future.
• F’: Your age in the future.

The statement, “I have twice the age you had when I had the age you have” means that my current age (N) is twice your age in the past (P’). So, N = 2P’.

And the statement, “When you’ll have the age I have, together we will have 63 years” tells us that in the future, when you reach my current age (F’ = N), together we’ll be 63 years old. So: F’ + F =63

Because we’ve established that N = 2P’, itmeans F’ = N = 2P’.

There is part of statement 1 that is also crucial: ….WHEN I HAD THE AGE YOU HAVE

The part/phrase “when I had the age you have” means that in the past, I was the age you are now. This makes P = N’, because P (my age at that time) is exactly the same as your current age, N’. In other words, we are saying that the age I had at some point in the past (P) is equal to your present age (N’).

So far, we have these equations:

1. N = 2P’
2. F’ = N = 2P’
3. P = N’
4. F’ + F =63

I hope we’re on the same page up to this point. Great! Let’s move on…

Since time moves the same for both of us, the difference between our ages never changes. So your future age minus your current age should be equal to my future age minus current age. So we can have:

F′−N′ = F−N

…which can also be written as F –F’ = N –N’ to mean thatthe number of years between our future ages is the same as the number of years between our current ages.

Going by the same analogy, the difference between your current age and your past age should also be equal to the difference between my current age and my past age. So, we can also have:

 N` – P` = N – P.

Now we have 6 equations:

1. N = 2P’
2. F’ = N = 2P’
3. P = N’
4. F’ + F =63
5. F′−N′ = F−N
6. N` – P` = N – P.

Let’s use them to solve the puzzle….

F’- N’ = F- N

but from equation (II) F’ = N= 2P’

So, 2P’- N’ = F = 2P’

and from equation (III), P = N’

Which means 2P’- P = F -2P’……………………….(VII)

but F = 63 – F’ (from equation (IV)

which can also be written as: F = 63 – 2P'(because F’ = N = 2p’)

Equation (VII) then becomes: 2P’-P = 63- 2P’ – 2P’, which we can break further as follows:

2P’ + 2P’ + 2P’ = 63 + P

6P’ = 63 + P

and P = 63 – 6P’…………..(VIII)

Let’s now focus on equation (VI): N’- P’ = N – P

from equation (III), we know that P = N’

so (VI) becomes P – P’ = N – P

but again N = 2P’

so P- P’ = 2P’- P

and by putting like terms together, we have: 2P = 3P’

and we can say that P = 3/2P’

In equation (VIII), we had: P = P = 3/2P’

so, 3/2P’ = P = 3/2P’

3P’ = 126 -6P’

9P’ = 126

P’= 14

Thus, your past age = 14 years

From equation (I), my current age = 2x 14 = 28 years

In equation (II), we had F’ = N = 2P’, which implies that your future age is also 28 years

Since when my future age is added to your future age sums we get a total of 63 years, (i.e F + F’ = 63), it means:

F + 28 (your future age) = 63

So F (my future age) = 63-28 = 35 years

If my current age is 28 years and my future is 35 years, it means F -N = 7

So, from equation (V), we can get your current age as follows:

F’ – N’ = F – N = 7

28 – N’ = 7

and N’ = 28-7 = 21

So my current age is 28 years and yours is 21 years.