Question

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? \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}

• A. 22.7
• B. 23.7
• C. 15.0
• D. 66.8

Hint:

In percentage-based pie chart problems, always compute actual values for each category, add them, and then divide by the grand total to get the required proportion.

Answer 1

The Correct Option is B

Step 1: Determine Grade III proportions. From the provided pie charts: - Universities classified as Grade III constitute 7% of the total 504 institutions.
- Colleges classified as Grade III constitute 23% of the total 25951 institutions.

Step 2: Calculate the exact number of Grade III institutions. \[\text{Universities (Grade III)} = \frac{7}{100} \times 504 = 35.28 \approx 35\] \[\text{Colleges (Grade III)} = \frac{23}{100} \times 25951 = 5968.73 \approx 5969\] The sum of Grade III institutions is therefore \(35 + 5969 = 6004\).

Step 3: Calculate the total number of institutions. \[\text{Total institutions} = 504 + 25951 = 26455\]

Step 4: Compute the overall percentage of Grade III institutions. \[\% = \frac{6004}{26455} \times 100\] \[= 22.7% \text{(approximate from preliminary calculation)}\] Upon precise recalculation: \[\frac{6004}{26455} \times 100 = 22.7 %\] A careful re-evaluation yields: \[\frac{35.28 + 5968.73}{26455} \times 100= \frac{6004.01}{26455} \times 100 = 22.7 %\] The question requires the answer to one decimal place. Consequently, the final result is 22.7%. \[\boxed{22.7 %}\]