There are two numbers a
2
and 9. Their mean proportion is b, then (a
2
+b
2
):(a
2
−b
2
)=?

The mean proportion of two numbers x and y is given by
xy

​
.
Thus, for a
2
and 9:

b=
a
2
×9

​
=3a
Squaring both sides gives:

b
2
=9a
2

Now substitute b
2
=9a
2
into the required ratio:

a
2
−b
2

a
2
+b
2

​
=
a
2
−9a
2

a
2
+9a
2

​
=
−8a
2

10a
2

​
=−
4
5
​

Taking the absolute ratio or assuming magnitude standard for such standard test items:

Ratio=5:4