Calculate Black shirts for S and T

For unit S, the ratio is 4:13, so total parts = 17. Black shirts = $\frac{4}{17} \times 3825 = 4 \times 225 = 900$. For unit T, the ratio is 4:9, so total parts = 13. Black shirts = $\frac{4}{13} \times 4875 = 4 \times 375 = 1500$.

$\text{Black}_S = 900, \quad \text{Black}_T = 1500$

Calculate total Black and total Production

Sum of black shirts = $900 + 1500 = 2400$. Sum of total production = $3825 + 4875 = 8700$.

$\text{Total Black} = 2400, \quad \text{Total Shirts} = 8700$

Calculate final percentage

Percentage = $\frac{2400}{8700} \times 100 = \frac{24}{87} \times 100 = \frac{8}{29} \times 100 = \frac{800}{29}\%$.

$\text{Result} = \frac{800}{29}\%$