Calculate Black shirts for Q and U

Unit Q produces $3150$ total with a ratio of $9:5$. Black shirts = $\frac{9}{14} \times 3150 = 2025$. Unit U produces $4950$ with a ratio of $11:7$. Black shirts = $\frac{11}{18} \times 4950 = 3025$. Total Black = $2025 + 3025 = 5050$.

$\text{Total Black} = 2025 + 3025 = 5050$

Calculate White shirts for P and Q

Unit P produces $5225$ with a ratio of $10:9$. White shirts = $\frac{9}{19} \times 5225 = 2475$. Unit Q produces $3150$ with a ratio of $9:5$. White shirts = $\frac{5}{14} \times 3150 = 1125$. Total White = $2475 + 1125 = 3600$.

$\text{Total White} = 2475 + 1125 = 3600$

Calculate the final ratio

The ratio of total black shirts ($5050$) to total white shirts ($3600$) is $\frac{5050}{3600}$. Dividing both by $50$, we get $101:72$.

$\frac{5050}{3600} = \frac{101}{72}$