We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of $N$ is $192$.

1. Problem Description

We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of $N$ is $192$.

2. Solution Steps

First, we set up the equation based on the given information:

$84\% \cdot N = 105\% \cdot (N-120)$

Convert percentages to decimals:

$0.84N = 1.05(N-120)$

Expand the right side:

$0.84N = 1.05N - 1.05 \cdot 120$

$0.84N = 1.05N - 126$

Move terms involving N to one side:

$1.05N - 0.84N = 126$

$0.21N = 126$

Solve for N:

$N = \frac{126}{0.21}$

$N = 600$

Now, we need to find what percentage of $N$ is $192$. Let's call that percentage $x$.

$x\% \cdot N = 192$

$x\% \cdot 600 = 192$

Convert percentage to a decimal:

$\frac{x}{100} \cdot 600 = 192$

Solve for $x$:

$6x = 192$

$x = \frac{192}{6}$

$x = 32$

3. Final Answer

The final answer is 32.