Question

Total number of students studying in institute Q is what percent of the total number of students studying in institute T?

• A. 150%
• B. 115%
• C. 125%
• D. 100%
• A. 66.66
• B. 73.33
• C. 83.33
• D. 78.33
• A. 5%
• B. 15%
• C. 30%
• D. 45%

Answer 1

The Correct Option is A

Finding the Required Percentage from the Pie Chart 

Step 1: Calculate the Number of Students in Each Institute

Total number of students = 4,800

• Students in Institute Q (12% of total): \[ \frac{12}{100} \times 4800 = 576 \]
• Students in Institute T (8% of total): \[ \frac{8}{100} \times 4800 = 384 \]

Step 2: Compute the Required Percentage

The required percentage is:

\[ \frac{576}{384} \times 100 \]

\[ = 1.5 \times 100 = 150\% \]

Final Answer:

Thus, the correct answer is 150% (Option A).

Answer 2

Finding the Required Percentage of Students 

Step 1: Express the Total Number of Students

Let the total number of students in each institute be a multiple of \( x \).

• For Institute Q: \[ \text{Total students} = 5x + 4x = 9x \]
• For Institute V: \[ \text{Total students} = 7x + 5x = 12x \]
• For Institute S: \[ \text{Total students} = 6x + 5x = 11x \]
• For Institute T: \[ \text{Total students} = 3x + 5x = 8x \]

Step 2: Compute the Required Percentage

Total students in Institutes Q and V:

\[ 9x + 12x = 21x \]

Total students in Institutes S and T:

\[ 11x + 8x = 19x \]

The required percentage is:

\[ \frac{\text{Total students in Q and V}}{\text{Total students in S and T}} \times 100 \]

\[ \frac{21x}{25x} \times 100 \]

\[ = \frac{21}{25} \times 100 = 83.33\% \]

Final Answer:

Thus, the correct answer is 83.33% (Option C).

Answer 3

Finding the Percentage Increase from the Pie Chart 

Step 1: Calculate the Number of Students in Each Institute

Total number of students = 4,800

• Students in Institute R (16% of total): \[ \frac{16}{100} \times 4800 = 768 \]
• Students in Institute U (11% of total): \[ \frac{11}{100} \times 4800 = 528 \]

Step 2: Compute the Percentage Increase

The percentage increase is given by:

\[ \frac{\text{Increase in students}}{\text{Original number of students}} \times 100 \]

Substituting the values:

\[ \frac{768 - 528}{528} \times 100 \]

\[ = \frac{240}{528} \times 100 \]

\[ \approx 45.45\% \]

Final Answer:

Thus, the correct answer is 45% (Option D).