Question

The following chart shows the percentage of students studying in different IITs in the year 2022. The ratio of male students to female students in each IIT is given. What is the total number of male students in all IITs put together?
The table below shows the percentage of students in different IITs, along with the ratio of male to female students in each IIT.

• A. 1865
• B. 2421
• C. 2025
• D. 1954
• E. 2179

Hint:

To calculate the total number of male students from the male: female ratio, first calculate the total number of students in each institution using the percentage, then apply the ratio to find the number of male students.

Answer 1

The Correct Option is B

Step 1: Calculate total number of students in each IIT.
We are given that the total number of students in all IITs combined is 4500. We can calculate the number of students in each IIT by using the percentage provided. \[ \text{Number of students in IIT Bombay} = 4500 \times 0.22 = 990 \] \[ \text{Number of students in IIT Delhi} = 4500 \times 0.18 = 810 \] \[ \text{Number of students in IIT Kanpur} = 4500 \times 0.21 = 945 \] \[ \text{Number of students in IIT Kharagpur} = 4500 \times 0.16 = 720 \] \[ \text{Number of students in IIT Madras} = 4500 \times 0.12 = 540 \] \[ \text{Number of students in IIT Roorkee} = 4500 \times 0.11 = 495 \] Step 2: Calculate the number of male students in each IIT.
We will now calculate the number of male students in each IIT using the given male to female ratios. - For IIT Bombay (Ratio 2:3), the total students are 990, and the male students are: \[ \text{Male students in IIT Bombay} = \frac{2}{5} \times 990 = 396 \] - For IIT Delhi (Ratio 12:17), the total students are 810, and the male students are: \[ \text{Male students in IIT Delhi} = \frac{12}{29} \times 810 = 334.48 \approx 334 \] - For IIT Kanpur (Ratio 7:5), the total students are 945, and the male students are: \[ \text{Male students in IIT Kanpur} = \frac{7}{12} \times 945 = 551.25 \approx 551 \] - For IIT Kharagpur (Ratio 5:4), the total students are 720, and the male students are: \[ \text{Male students in IIT Kharagpur} = \frac{5}{9} \times 720 = 400 \] - For IIT Madras (Ratio 11:5), the total students are 540, and the male students are: \[ \text{Male students in IIT Madras} = \frac{11}{16} \times 540 = 371.25 \approx 371 \] - For IIT Roorkee (Ratio 21:3), the total students are 495, and the male students are: \[ \text{Male students in IIT Roorkee} = \frac{21}{24} \times 495 = 458.25 \approx 458 \] Step 3: Total number of male students.
Now, we will sum the number of male students from all IITs: \[ \text{Total male students} = 396 + 334 + 551 + 400 + 371 + 458 = 2421 \] Step 4: Conclusion.
Therefore, the total number of male students in all IITs put together is \(2421\), so the correct answer is (B).