What are their ages?

Question

Two friends meet to celebrate their birthdays, which fall on the same date but different years. "This is a very special birthday." says one of them, "because whilst collectively we are 63 years old, I am also twice as old as you were when I was as old as you are now."

What are their ages.

Answer 1

27 and 36.... i think....

Answer 2

According to logic,it should be 27,36

Answer 3

27 and 36

27 + 36 = 63

when he was 27 was 9 years ago, 27 - 9 = 18

twice 18 is 36

Answer 4

36 and 27

Answer 5

One of the people would be 21 years of age and the other would be 42 years of age

Answer 6

uhmmm...the 31 and 25???????

Answer 7

We know that the ages add up to 63

We also know that there is a relationship between the two ages, such that there is a point in time, where the younger person's age, is 1/2 the current age of the older person (or the older person is twice as old as the younger person, at that point in time)

This means that there is a common factor between the ages.

The common factors for 63 are 1, 7 , 9 and 63.

Multiples of these factors, must add to 63

By inspection, the options are:

a) (5 x 7) + (4 x 7) = 63 (i.e 35 and 28)

b) (4 x 9) + (3 x 9) = 63 (i.e 36 and 27)

To satisfy the last condition, the older person's age must be an even number.

Therefore b) is correct.

CHECK:

27 + 36 = 63

1/2 of 36 is 18.

9 years ago, the older person's age = the younger person's current age (27)

The younger persons age at the point in time is 18, which is 1/2 of 36.

Answer 8

x and y are current ages.

(x - a) and (y - a) are the prior ages ("a" years ago).

"collectively we are 63 years old"

x + y = 63

"... I am also twice as old as you were ..."

x = 2 (y - a)

" ... when I was as old as you are now ..."

(x - a) = y

Multiply 3rd equation by -2 and add to 2nd:

i) -x + 4a = 0

Now add this to 1st:

ii) y + 4a = 63

Multiply 3rd equation by -1 and add to 2nd:

iii) - y + 3a = 0

Add to iii):

iv) 7a = 63

a = 9, so the time in the past was 9 years ago.

Substituting into i),

x = 36

So, substituting into 1st equation,

y = 27

Answer 9

36 and 27

9 years ago the younger one was 18, thus the old one is now twice as old he was back then.

Answer 10

Yeah Disco got this one, hes the only one who did. Its confusing, but the answer is NOT 42 and 21.

Most people didn't read the question right

36 and 27