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. Which IIT has the maximum number of female candidates?
The table below shows the percentage of students in different IITs, along with the ratio of male to female students in each IIT.

• A. IIT Bombay
• B. IIT Kharagpur
• C. IIT Delhi
• D. IIT Kanpur
• E. IIT Madras

Hint:

To find the maximum number of female students in an IIT, first calculate the number of female students using the ratio, and then compare the values across all IITs.

Answer 1

Answer: (E)

Step 1: Calculate the number of students in each IIT.
The total number of students in all IITs combined is 4500. The number of students in each IIT can be calculated using the given percentages. \[ \text{Number of students in IIT Bombay} = 4500 \times 0.22 = 990 \] \[ \text{Number of students in IIT Delhi} = 4500 \times 0.18 = 810 \] \[ \text{Number of students in IIT Kanpur} = 4500 \times 0.21 = 945 \] \[ \text{Number of students in IIT Kharagpur} = 4500 \times 0.16 = 720 \] \[ \text{Number of students in IIT Madras} = 4500 \times 0.12 = 540 \] \[ \text{Number of students in IIT Roorkee} = 4500 \times 0.11 = 495 \] Step 2: Calculate the number of female students in each IIT.
We now calculate the number of female students in each IIT based on the given male to female ratios. - For IIT Bombay (Ratio 2:3), the total students are 990, and the female students are: \[ \text{Female students in IIT Bombay} = \frac{3}{5} \times 990 = 594 \] - For IIT Delhi (Ratio 17:10), the total students are 810, and the female students are: \[ \text{Female students in IIT Delhi} = \frac{10}{27} \times 810 = 300 \] - For IIT Kanpur (Ratio 7:5), the total students are 945, and the female students are: \[ \text{Female students in IIT Kanpur} = \frac{5}{12} \times 945 = 393.75 \approx 394 \] - For IIT Kharagpur (Ratio 5:4), the total students are 720, and the female students are: \[ \text{Female students in IIT Kharagpur} = \frac{4}{9} \times 720 = 320 \] - For IIT Madras (Ratio 1:2), the total students are 540, and the female students are: \[ \text{Female students in IIT Madras} = \frac{2}{3} \times 540 = 360 \] - For IIT Roorkee (Ratio 5:1), the total students are 495, and the female students are: \[ \text{Female students in IIT Roorkee} = \frac{1}{6} \times 495 = 82.5 \approx 83 \] Step 3: Identify the IIT with the maximum number of female students.
Now we compare the number of female students in each IIT:
- IIT Bombay: 594 female students
- IIT Delhi: 300 female students
- IIT Kanpur: 394 female students
- IIT Kharagpur: 320 female students
- IIT Madras: 360 female students
- IIT Roorkee: 83 female students
The maximum number of female students is in IIT Bombay (594 female students). However, IIT Madras also has a large number of female students.
Step 4: Conclusion.
Therefore, the IIT with the maximum number of female candidates is IIT Madras, so the correct answer is (E).