Solution:

Given ratio compounded of 4:5 and sub-duplicate of “a”: 9 is 8:15.

Let’s take the ratio compounded of 4:5 as a single ratio and solve for the sub-duplicate of “a”: 9 ratio.

Ratio compounded of 4:5 = (4x)/(5x)

Sub-duplicate of “a”: 9 = (√a)/(3)

According to the question, the ratio compounded of 4:5 and sub-duplicate of “a”: 9 is 8:15.

Therefore, (4x)/(5x) : (√a)/(3) = 8/15

Cross-multiplying, we get:

(4x) * 15 = (5x) * 8(√a)/3

60x = 40(√a)

√a = (60x)/40

√a = (3/2) * x

Squaring on both sides, we get:

a = 9/4 * x^2

Now, we need to find the value of “a”.

To find the value of “a”, we need to find the value of “x”.

Let’s take the denominator of the ratio compounded of 4:5, i.e., 5x, as a common denominator.

Therefore, (4x)/(5x) = 4/5

According to the question, the ratio compounded of 4:5 and sub-duplicate of “a”: 9 is 8:15.

Therefore, 4/5 : (√a)/(3) = 8/15

Cross-multiplying, we get:

(4/5) * 15 = (√a) * 8/3

12 = (8/3) * √a

√a = (3/2) * 12

√a = 18

Now, substituting the value of √a in the equation a = 9/4 * x^2, we get:

a = 9/4 * x^2 = 9/4 * (18/3)^2

a = 81

Therefore, the value of “a” is 81.

(4 root a/ 5 root 9) = 8/15