Question 977409
The ratio of age of a man and his wife is 4:3 ...at the time of marriage, the ratio was 5:3 and after 4 yrs the ratio will become 9:7... How many yrs ago were they married?

<pre>
Let the number of years ago they were married be y years ago.
</pre>
The ratio of age of a man and his wife is 4:3 
<pre>
So there is some number k, so that the man's age is now 4k 
and the wife's age is now 3k 
</pre>
...at the time of marriage, the ratio was 5:3 
<pre>
{{{(4k-y)/(3k-y)}}}{{{""=""}}}{{{5/3}}}

{{{3(4k-y)}}}{{{""=""}}}{{{5(3k-y)}}}

{{{12k-3y}}}{{{""=""}}}{{{15k-5y}}}

{{{2y}}}{{{""=""}}}{{{3k}}}
</pre>
and after 4 yrs the ratio will become 9:7... 
<pre>
{{{(4k+4)/(3k+4)}}}{{{""=""}}}{{{9/7}}}

{{{7(4k+4)}}}{{{""=""}}}{{{9(3k+4)}}}

{{{28k+28}}}{{{""=""}}}{{{27k+36}}}

{{{k}}}{{{""=""}}}{{{8}}}

Substitute that in 

{{{2y}}}{{{""=""}}}{{{3k}}}
{{{2y}}}{{{""=""}}}{{{3(8)}}}
{{{2y}}}{{{""=""}}}{{{24}}}
{{{y}}}{{{""=""}}}{{{12}}}

Answer:  12 years ago.

Checking:

The man is 4k = 4(8) = 32
The wife is 3k = 3(8) = 24
</pre>
The ratio of age of a man and his wife is 4:3
<pre>
32/24 = 4/3, that checks.
</pre>
...at the time of marriage, the ratio was 5:3
<pre>
They married 12 years ago when he was 20 and she was only 12. (WOW!)

20/12 = 5/3, that checks.  (WOW!!)
</pre>
and after 4 yrs the ratio will become 9:7...
<pre>
He will be 36 and she will be 28

36/28 = 9/7, that checks.

That's correct but I think it's terrible that your teacher would assign 
a problem that implies that a girl was married at age 12, even if it is
only a math problem !!!  

Edwin</pre>