Question

What is the ratio of the number of female students in institute S and that of male students in institute R?

• A. 3 : 7
• B. 2 : 3
• C. 1 : 1
• D. 3 : 2
• A. 2438
• B. 1056
• C. 2117
• D. 2108

Answer 1

The Correct Option is D

Calculating the Required Ratio from the Given Pie Chart: 

Step 1: Total Number of Students

The total number of students is 4,800.

Step 2: Number of Students in Each Institute

• Institute S (16% of total students): \[ \frac{16}{100} \times 4800 = 768 \text{ students} \]
• Institute R (13% of total students): \[ \frac{13}{100} \times 4800 = 624 \text{ students} \]

Step 3: Calculate Male and Female Students in Each Institute

Institute S (Male : Female = 6:5)

• Total students = 768
• Male students: \[ \frac{6}{11} \times 768 = 418.18 \approx 418 \]
• Female students: \[ 768 - 418 = 350 \]

Institute R (Male : Female = 5:7)

• Total students = 624
• Male students: \[ \frac{5}{12} \times 624 = 260 \]
• Female students: \[ 624 - 260 = 364 \]

Step 4: Required Ratio

The required ratio of female students in Institute S to male students in Institute R is:

\[ \frac{\text{Female students in S}}{\text{Male students in R}} = \frac{350}{260} \]

Simplifying: \[ \frac{350}{260} = \frac{35}{26} = \mathbf{3:2} \]

Final Answer:

Thus, the correct answer is (D) 3 : 2.

Answer 2

Calculating the Total Number of Male Students:

Step 1: Find the Total Number of Students in Each Institute

The total number of students is 4,800. Using the percentage distribution: 

• Institute P: \[ \frac{18}{100} \times 4800 = 864 \]
• Institute Q: \[ \frac{16}{100} \times 4800 = 768 \]
• Institute R: \[ \frac{12}{100} \times 4800 = 576 \]
• Institute S: \[ \frac{8}{100} \times 4800 = 384 \]
• Institute T: \[ \frac{22}{100} \times 4800 = 1056 \]
• Institute U: \[ \frac{13}{100} \times 4800 = 624 \]
• Institute V: \[ \frac{11}{100} \times 4800 = 528 \]

Step 2: Calculate the Number of Male Students in Each Institute

Using the given male-to-female ratios:

• Male Students in P (\( 7:9 \)): \[ \frac{7}{7+9} \times 864 = \frac{7}{16} \times 864 = 378 \]
• Male Students in Q (\( 5:4 \)): \[ \frac{5}{5+4} \times 768 = \frac{5}{9} \times 768 = 427 \]
• Male Students in R (\( 5:7 \)): \[ \frac{5}{5+7} \times 576 = \frac{5}{12} \times 576 = 240 \]
• Male Students in S (\( 6:5 \)): \[ \frac{6}{6+5} \times 384 = \frac{6}{11} \times 384 = 210 \]
• Male Students in T (\( 3:5 \)): \[ \frac{3}{3+5} \times 1056 = \frac{3}{8} \times 1056 = 396 \]
• Male Students in U (\( 7:4 \)): \[ \frac{7}{7+4} \times 624 = \frac{7}{11} \times 624 = 397 \]
• Male Students in V (\( 7:5 \)): \[ \frac{7}{7+5} \times 528 = \frac{7}{12} \times 528 = 390 \]

Step 3: Total Male Students

\[ 378 + 427 + 240 + 210 + 396 + 397 + 390 = 2438 \]

Final Answer:

Thus, the correct answer is (A) 2438.