The problem states that 10% of 20% of a is equal to 30% of 40% of b. We need to find what percentage of $(3a+2b)$ is $(2a-3b)$.

1. Problem Description

The problem states that 10% of 20% of a is equal to 30% of 40% of b. We need to find what percentage of $(3a+2b)$ is $(2a-3b)$.

2. Solution Steps

First, we translate the given information into an equation:

$0.10 * 0.20 * a = 0.30 * 0.40 * b$

$0.02a = 0.12b$

Dividing both sides by 0.02, we get:

$a = 6b$

Now, we want to find what percentage of $(3a+2b)$ is $(2a-3b)$. Let this percentage be $x$. So,

$x\% * (3a + 2b) = (2a - 3b)$

$\frac{x}{100} * (3a + 2b) = (2a - 3b)$

Substitute $a = 6b$ into the equation:

$\frac{x}{100} * (3(6b) + 2b) = (2(6b) - 3b)$

$\frac{x}{100} * (18b + 2b) = (12b - 3b)$

$\frac{x}{100} * (20b) = 9b$

Divide both sides by $b$ (assuming $b \neq 0$):

$\frac{x}{100} * 20 = 9$

$\frac{20x}{100} = 9$

$\frac{x}{5} = 9$

$x = 9 * 5$

$x = 45$

Therefore, $(2a - 3b)$ is 45% of $(3a + 2b)$.

3. Final Answer

45%