A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

The correct option is 22.7.

Step-by-step Explanation:

1. Identify the total number of higher education institutions:
From the problem description, we have:
Number of universities = 504
Number of colleges = 25,951
Therefore, the total number of institutions is:
$$\text{Total Institutions}=504+\mathrm{25,951}=\mathrm{26,455}$$

2. Determine the number of Grade III institutions from the pie charts:
By analyzing the provided pie charts:
- The pie chart for Universities shows that Grade III accounts for 7% of the total universities.
- The pie chart for Colleges shows that Grade III accounts for 23% of the total colleges.

Let's calculate the absolute number of Grade III universities:
$$\text{Grade III Universities}=7\%\text{ of }504=\frac{7}{100}\times 504=35.28$$
Next, calculate the absolute number of Grade III colleges:
$$\text{Grade III Colleges}=23\%\text{ of }\mathrm{25,951}=\frac{23}{100}\times \mathrm{25,951}=\mathrm{5,968.73}$$
Sum these two values to find the total number of Grade III institutions:
$$\text{Total Grade III Institutions}=35.28+\mathrm{5,968.73}=\mathrm{6,004.01}$$

3. Calculate the overall percentage of Grade III institutions:
We find the percentage by dividing the total Grade III institutions by the total number of institutions, then multiplying by 100:
$$\text{Percentage of Grade III Institutions}=\left(\frac{\mathrm{6,004.01}}{\mathrm{26,455}}\right)\times 100\%$$
$$\approx 0.22695\times 100\%\approx 22.695\%$$
Rounding to one decimal place, we obtain 22.7%.