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' When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'

His sister said: 'When I am as old as you were when you were twice as old as I was, you will be just a year older than you are.'

How old were they?

they were not the same age.

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' When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'

His sister said: 'When I am as old as you were when you were twice as old as I was, you will be just a year older than you are.'

How old were they?

they were not the same age.

er. this is difficult I m confused by everything!

64=ken

22= sis

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' When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'

His sister said: 'When I am as old as you were when you were twice as old as I was, you will be just a year older than you are.'

How old were they?

they were not the same age.

Ken is 13

his sister is 7

So we let Ken's age be x and his sister's age be y

The first part of the first statement is rougly translated to "sister's age two years ago" which we represent as y-2

The second part is "sister is 1/3 of (my age + 2)" So we set them equal where

y-2 = (1/3)(x+2)

3y-6 = x+2

3y-x = 8

Now we look at the second statement. There existed a time 'n' years ago where (x-n)/(y-n) = 2..... (x was twice as old as y)

Edited by James T
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Hmm it cut me off as I was trying to finish editing in my work:

According to the second part of the second statement, at the given x-n years from the previous part, Ken is x-1 years old. This implies that n = 1.

So one year ago, Ken was twice as old as his sister.

(x-1)/(y-1) = 2

x-1 = 2y - 2

2y -x = 1

Taking both equations and subtracting:

3y-x = 8

2y-x=1

y = 7

plugging this back in gives x = 13.

So ken is 13 while his sister is 7.

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Hmm it cut me off as I was trying to finish editing in my work:

According to the second part of the second statement, at the given x-n years from the previous part, Ken is x-1 years old. This implies that n = 1.

So one year ago, Ken was twice as old as his sister.

(x-1)/(y-1) = 2

x-1 = 2y - 2

2y -x = 1

Taking both equations and subtracting:

3y-x = 8

2y-x=1

y = 7

plugging this back in gives x = 13.

So ken is 13 while his sister is 7.

I'm sorry, but that's not it you were the closest though

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I'm sorry, but that's not it you were the closest though

Hmmm I reread the question and I must think that it is a bit impossible.

For the first statement follows this equation:

7x-9y = -8

where x is Ken's age and y is his sister's age.

solutions include (4,4) (22,18) (40,32) (58, 46)... and so on

A quick check shows that all of them satisfy the first part.

The second statement implies this equation:

2x-3y = 1

solutions include (2,1) (5,3) (8,5) (11,7) (14,9) (17,11) (20,13)... and so on.

A quick check confirms that all of them satisfy the second part.

Now if you solve the equations together, the only working solution for both of them is (-11, -23/3). Since ages cannot be negative nor fraction, there are no solutions to this problem.

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1 and 2?

Yes, I agree that it does satisfy the second statement. However the first statement "When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'"

When Ken was two year's younger, he would be 0 years old and his sister wasn't even born yet.

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Yes, I agree that it does satisfy the second statement. However the first statement "When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'"

When Ken was two year's younger, he would be 0 years old and his sister wasn't even born yet.

Ken=10

Sister=8

Ken=x sister=y

When Ken was two years younger, his sister was (y-2).

When Ken was(y-2) his sister was (2y-x-2). In two years' time ken would be(x+2) One third of thar is (x+2)/3. Combining gives 4x-6y=-8, so -3y=-4.

Working back from his sisters words-"When you were twice as ol as I was" -Ken was(2x-@y) and his sister was(x-y). When his sister was (2x-2y+3), Ken was #x-#y+3). When his sister is (3x-3y+3,Ken will be (4x-4y-3).

Hence, 4x-4y-3 = x+1

so #x-$y = -2

Combining: x=10

y=8

So, Ken was 10 years old and his sister was 8.

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Ken=10

Sister=8

Ken=x sister=y

When Ken was two years younger, his sister was (y-2).

When Ken was(y-2) his sister was (2y-x-2). In two years' time ken would be(x+2) One third of thar is (x+2)/3. Combining gives 4x-6y=-8, so -3y=-4.

Working back from his sisters words-"When you were twice as ol as I was" -Ken was(2x-@y) and his sister was(x-y). When his sister was (2x-2y+3), Ken was #x-#y+3). When his sister is (3x-3y+3,Ken will be (4x-4y-3).

Hence, 4x-4y-3 = x+1

so #x-$y = -2

Combining: x=10

y=8

So, Ken was 10 years old and his sister was 8.

Well the ages 10 and 8 match the first part of the statement. However look at the second statement: "His sister said: 'When I am as old as you were when you were twice as old as I was, you will be just a year older than you are.'"

Part by part: "when you were twice as old as I was"

that can only occur when his sister is 2 and Ken is 4.

"When I am as old as you were"

So when his sister was 4 (ken's age)

Ken would be 6

"you will be just a year older than you are"

That implies that Ken's current age is 5. Which is not true because the answer says that he is 10.

So that answer doesn't work.

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Can't be 10 and 8.

"When I was as old as you were when I was two years younger than I am now..." can be restated as, "Two years ago, when I was as old as you were...", indicating that two years ago, they were the same age. Putting it another way, if the given answer is actually 10 and 8, then the statement is, "When I was as old as you were two years ago when I was 8 and you were 6......." But if they are the same age, say 10, then the statement becomes, "Two years ago, when I was as old as you were, which was 8, I was also 8..."

If they were the same age, based on the first premise, then balance of the riddle is violated.

I believe that this riddle has no possible answer.

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Can't be 10 and 8.

"When I was as old as you were when I was two years younger than I am now..." can be restated as, "Two years ago, when I was as old as you were...", indicating that two years ago, they were the same age.

While I agree that this is unsolvable, I don't agree on the reason stated.

"When I was as old as you were when I was two years younger than I am now..." can be restated as, "Two years ago, when I was as old as you were...", indicating that two years ago, they were the same age...

I don't believe this to be true. I'd say that this could be restated as: "When I was the age you were 2 years ago..." which means, when he was that age, she would be equally younger.

However, I do agree that this cannot be solved, and I think James T describes the reason very well.

Edited by uhre
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Second part of the question can't make any sense. Because it starts with "when I'm as old as ...."

When you say "I am ", you imply "today".

If you imply future, you say "I will be",

or past, "I was".

After wasting a half hour, I saw that my english is incapable to solve this.

First part of the question is concordant with 8/10 ages,

but I couldn't even check the second part???

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Second part of the question can't make any sense. Because it starts with "when I'm as old as ...."

When you say "I am ", you imply "today".

If you imply future, you say "I will be",

or past, "I was".

After wasting a half hour, I saw that my english is incapable to solve this.

First part of the question is concordant with 8/10 ages,

but I couldn't even check the second part???

I dissagree. She is describing a time in HER future. Look at it this way, "In twenty years, when I am 40 years old..."

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I dissagree. She is describing a time in HER future. Look at it this way, "In twenty years, when I am 40 years old..."

You're right. I couldn't decipher the second part, and thought that its reason was what I posted.

If you're able to understand the second part, can you check 8/10 years, or what the answer is?

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You're right. I couldn't decipher the second part, and thought that its reason was what I posted.

If you're able to understand the second part, can you check 8/10 years, or what the answer is?

Just read James T's spoiler (last on page 1). That checks 8/10 against the 2nd part - and invalidates the OP, as I see it.

Edited by uhre
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does not exist.

If the siblings are 1 year apart, brother is twice the sisters age at 2, so she is now 1 and he is now 2 and in 2 years he will be 4 which is not wholely divisible by 3.

If the siblings are 2 years apart, brother is twice the sisters age at 4, so she is now 3 and he is now 5 and in 2 years he will be 7 which is not wholely divisible by 3.

If the siblings are 3 years apart, brother is twice the sisters age at 6, so she is now 5 and he is now 8 and in 2 years he will be 10 which is not wholely divisible by 3.

If the siblings are 4 years apart, brother is twice the sisters age at 8, so she is now 7 and he is now 11 and in 2 years he will be 13 which is not wholely divisible by 3.

If the siblings are 5 years apart, brother is twice the sisters age at 10, so she is now 9 and he is now 14 and in 2 years he will be 16 which is not wholely divisible by 3.

If the siblings are 6 years apart, brother is twice the sisters age at 12, so she is now 11 and he is now 17 and in 2 years he will be 19 which is not wholely divisible by 3.

If the siblings are 7 years apart, brother is twice the sisters age at 14, so she is now 13 and he is now 20 and in 2 years he will be 22 which is not wholely divisible by 3.

And so on, always leaving a remainder of 1/3...

Unless we are interpreting the wording incorrectly or a non-whole number/negative solution is acceptable this is unsolvable as stated.

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Here's what I came up with. I agree with the others who say there's no answer, at least if I'm interpreting the English in this question correctly.

The time they're talking about in the first clause of the brother's statement is:

When I was as old as you were (when I was two years younger than I am now),

When I was as old as you were two years ago,

Brother - TimeAgo = Sister - 2

TimeAgo = Brother - Sister + 2

...you were a third as old as I will be in two year's time

3 (Sister - TimeAgo) = Brother + 2

3 (Sister - Brother + Sister - 2) = Brother + 2

6 Sister - 3 Brother - 6 = Brother + 2

6 Sister - 4 Brother = 8

3 Sister - 2 Brother = 4

The time they're talking about in the first clause of the sister's statement is:

When I am (as old as you were when you were twice as old as I was)

When I am (twice the difference between our ages),

Sister + TimeAhead = 2 (Brother - Sister)

TimeAhead = 2 Brother - 3 Sister

...you will be just a year older than you are

Brother + TimeAhead = Brother + 1

2 Brother - 3 Sister = 1

3 Sister - 2 Brother = -1

Combining the bottom lines from each of the above, 4 = -1 :huh:

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These two statements can be simplified into: (K is Ken and S is Sister)

A. 2 years from now I will be 3 times as old as you were two years ago.

K+2=3(S-2)

K=3S-8

B. In a year I will be twice as old as I am now.

2S=S+1

S=1

Solving:

Ken equals 3 times his sister’s age less 8.

Ken’s quite precocious older sister is a wee lass of 1, while Ken won’t even be conceived until she is 5 plus. I certainly would have liked to have witnessed this conversation.

' When I was as old as you were when I was two years younger than I am now,' Ken told his sister, 'you were a third as old as I will be in two years' time.'

His sister said: 'When I am as old as you were when you were twice as old as I was, you will be just a year older than you are.'

How old were they?

]

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