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? 

 

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

Hint:

When dealing with percentages from different totals (like universities and colleges here), never average the percentages directly. Always calculate the actual values for each group first, then sum them up, and finally calculate the overall percentage based on the grand total.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks for the overall percentage of Grade III institutions. To find this, we first need to calculate the total number of Grade III institutions (universities + colleges) and divide it by the total number of all institutions.
Step 2: Key Formula or Approach:
\[ \text{Overall Percentage} = \left( \frac{\text{Total Grade III Institutions}}{\text{Total All Institutions}} \right) \times 100 \] Step 3: Detailed Calculation:
1. Calculate the number of Grade III universities:
From the pie chart, 7% of universities are Grade III.
\[ \text{Number of Grade III universities} = 7% \text{ of } 504 = 0.07 \times 504 = 35.28 \] 2. Calculate the number of Grade III colleges:
From the pie chart, 23% of colleges are Grade III.
\[ \text{Number of Grade III colleges} = 23% \text{ of } 25951 = 0.23 \times 25951 = 5968.73 \] 3. Calculate the total number of Grade III institutions:
\[ \text{Total Grade III} = 35.28 + 5968.73 = 6004.01 \] 4. Calculate the total number of all institutions:
\[ \text{Total Institutions} = 504 (\text{universities}) + 25951 (\text{colleges}) = 26455 \] 5. Calculate the final percentage:
\[ \text{Percentage of Grade III Institutions} = \left( \frac{6004.01}{26455} \right) \times 100 \] \[ \text{Percentage} \approx 0.22695 \times 100 \approx 22.695% \] 6. Round to one decimal place:
\[ 22.695% \approx 22.7% \] Step 4: Final Answer:
The percentage of higher education institutions that fall into Grade III is 22.7%.
Step 5: Why This is Correct:
The calculation correctly determines the absolute number of Grade III institutions from both categories before finding the overall percentage. Simply averaging the percentages (7% and 23%) would be incorrect because the base numbers (504 and 25951) are vastly different.