Question

at the time of marriage a man was 6 years older than his wife but 12 years after his marriage his age was 6/5 of the age of his wife .what were their ages at the time of marriage

Answer 1

Let's assume wife age=x
So,husband age =x+6
After 12 year of marriage
Wife's age=(x+12)years
Husband's age=(x+6+12)
=(x+18)
$\frac{6}{5}(x + 12) = (x + 18) \\ 6(x + 12) = 5(x + 18) \\ 6x + 72 = 5x + 90 \\ x = 18$
Hence,
Wife's age was 18
And husband's was 18+6=24

Answer 2

Wife is 18 years and Husband is 24 Years

Step-by-step explanation:

• Let the age of Wife be 'x' years

• Then the Age of husband will be x + 6 as per question

Now, the question has been forwarded to 12 Years.

As per question,  

Age of Wife will be (x + 12) years

and age of husband will be (x + 6) + 12 years

= (x + 18) years

Finally the age of husband is $\frac {6}{5}$ of wife's age and ages of both becomes equal

According to question,

$\frac {6}{5} \times (x + 12) = (x + 18)$

⇒ $6 \times (x + 12) = 5 \times (x + 18)$

⇒ 6x + 72 = 5x + 90

⇒ 6x - 5x = 90 - 72

⇒ x = 18

So, Age of Wife is 18 years and that of Husband is 18 + 6 = 24 Years