A man is twice as old as his wife was when he was the same age as she is now. She is 30, how old is he?

->

A man is twice as old as his wife was when he was 30. She is 30, how old is he?

->

When the man was 30, his wife was at such an age y that he is now aged 2y.

->

When m was 30, w was y, m is now 2y.

->

"When the man m was 30, his wife w was y years old. m is now 2y years old."

So we need to find 2y. The first facts to note are:

m = 2y

->

y = m/2

If:

m = 30

Then:

y = m/2 = 30/2 = 15

->

m = 30

The man and his wife are both 30. Although it may look like the man was 30 when his wife was 15, this is not so because the statement allows for two different points in time - "...his wife was...".

I realise that I state the obvious by saying: "If: m = 30 Then: ... m = 30"! But isn't this what the original statement is saying in disguise?

The man's current age, M_{a}, is his wife's current age, W_{a}, plus their age difference d:

M_{a} = W_{a} + d.

Now, d years ago the man was the same age as his wife is now and she was (W_{a} - d) years old

Given: M_{a} = 2(W_{a} - d ) so

W_{a} + d = 2(W_{a} - d ).

30 + d = 60 - 2d ; 3d = 30; d = 10.

M_{a} = 30 + 10 = 40.

Nasty this one: hard to write down an expression for man's age and even harder to say why in English that maybe I can understand 10 minutes later. Using a subscript notation makes things easier maybe?

## Comments

## New comment

PS Please show your working## New comment

I *think* I have it.

First, the statement can be simplified thus:

A man is twice as old as his wife was when he was the same age as she is now. She is 30, how old is he?

->

A man is twice as old as his wife was when he was 30. She is 30, how old is he?

->

When the man was 30, his wife was at such an age y that he is now aged 2y.

->

When m was 30, w was y, m is now 2y.

->

"When the man m was 30, his wife w was y years old. m is now 2y years old."

So we need to find 2y. The first facts to note are:

m = 2y

->

y = m/2

If:

m = 30

Then:

y = m/2 = 30/2 = 15

->

m = 30

The man and his wife are both 30. Although it may look like the man was 30 when his wife was 15, this is not so because the statement allows for two different points in time - "...his wife was...".

I realise that I state the obvious by saying: "If: m = 30 Then: ... m = 30"! But isn't this what the original statement is saying in disguise?

Dave

## New comment

But is that right?

If both are 30, he isn't twice as old as his wife was when he was the same age (30) as she is now (30) .

## New comment

Richard Walker: "But is that right?"

Certainly not, otherwise you would have told me it was!

A man is twice as old as his wife was when he was 30. She is 30, how old is he?

When the man was 30, his wife was at such an age y that he is now aged 2y.

Once upon a time:

w = y

m = 30

Currently:

w = 30

m = 2y

w has increased by 30 - y

m has increased by 2y - 30

The difference between their ages will always be the same, so:

30 - y = 2y - 30

3y = 60

y = 60/3 = 20

So the man is 40.

I hope you're not compiling any exam papers this year are you Richard?

Dave

## New comment

40 looks good!

I've always liked this puzzle, which I learned at an OU residential school.

## New comment

A man is twice as old as his wife was when he was the same age as she is now. She is 30, how old is he?

ok we have 2 points of time Previous and Now:

2 x WifePreviousAge = 30 PreviousManAge

WifePreviousAge = 15

WifeAgeNow is 30 (15 years later) = 30 PreviousManAge

ManAgeNow is 45 (15 years later)

Finally:

A man is twice x (15=WifePreviousAge) = when he was(30 PreviousManAge) = same age as she is now (WifeAgeNow = 30). She is 30, how old is he?

ManAgeNow is 45 (15 years later)

## Errm? Errm?

The man's current age, M

_{a}, is his wife's current age, W_{a}, plus their age difference d:M

_{a}= W_{a}+ d.Now, d years ago the man was the same age as his wife is now and she was (W

_{a}- d) years oldGiven: M

_{a}= 2(W_{a}- d ) soW

_{a}+ d = 2(W_{a}- d ).30 + d = 60 - 2d ; 3d = 30; d = 10.

M

_{a}= 30 + 10 = 40.Nasty this one: hard to write down an expression for man's age and even harder to say why in English that maybe I can understand 10 minutes later. Using a subscript notation makes things easier maybe?

## New comment

don't do maths but I get 45 in my head as follows

half of 30 is 15. So add 15 to 30 = 45

He is 45, she is 30.

I take it that this is wrong somehow and should be mathematically worked out? LOL

## New comment

Nice puzzle

1. List variables:

pastMan = 30pastWife = xnowMan = 2xnowWife = 302. Difference between now-ages and past-ages must be equal. So we can write:

(nowMan - pastMan) = (nowWife - pastWife)Which equates to:

(2x - 30) = (30 - x)3. Bring like terms together:

(2x + x) = (30 + 30)Therefore:

x = (60 / 3) = 204. Since newMan = 2x, the husband is now 40 years old.