Given that,
- Number of universities in a country $=504$
- Number of colleges in a country $=25951$
The number of universities that fall into Grade III $=7\% \text{ of } 504 = \dfrac{7}{100} \times 504 = 35.28$
The number of colleges that fall into Grade III $=23\% \text{ of } 25951 = \dfrac{23}{100} \times 25951 = 5968.73$
Thus, required percentage $=\dfrac{\text{Total number of universities and colleges that fall into grade III}}{\text{Total number of universities and colleges}} \times 100\%$
$= \dfrac{35.28 + 5968.73}{504 + 25951} \times 100\% = \dfrac{6004.01}{26455} \times 100\%$
$= 0.2269518 \times 100\% = 22.69518\% \approx 22.7\%.$
Correct Answer: A