1. The problem states that Uche and Chidi shared a sum of money in the ratio $m:n$. 2. Chidi's share corresponds to the part $n$ in the ratio, and it is given as 4200. 3. Since the total parts are $m + n$, the total sum shared is proportional to $m + n$ parts. 4. To find Uche's share, which corresponds to $m$ parts, we use the ratio: $$\text{Uche's share} = \frac{m}{n} \times \text{Chidi's share}$$ 5. Substituting Chidi's share as 4200, we get: $$\text{Uche's share} = \frac{m}{n} \times 4200 = 4200 \frac{m}{n}$$ 6. Therefore, the correct answer is option (c) $4200 \frac{m}{n}$.