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. The number of female students in IIT Kanpur is what percent of the total number of students in it?
The table below shows the percentage of students in different IITs, along with the ratio of male to female students in each IIT.

• A. 55
• B. 35
• C. 45
• D. 42
• E. 32

Hint:

To calculate the percentage of female students from a given ratio, first calculate the total number of students, then use the ratio to find the number of female students, and finally calculate the percentage.

Answer 1

The Correct Option is D

Step 1: Calculate total number of students in IIT Kanpur.
We are given that the total number of students in all IITs combined is 4500. The percentage of students in IIT Kanpur is 21%, so we can calculate the total number of students in IIT Kanpur: \[ \text{Number of students in IIT Kanpur} = 4500 \times 0.21 = 945 \] Step 2: Calculate the number of female students in IIT Kanpur.
The male to female ratio in IIT Kanpur is 7:5. This means for every 12 students, 5 are female. So, the number of female students in IIT Kanpur can be calculated as: \[ \text{Female students in IIT Kanpur} = \frac{5}{12} \times 945 = 393.75 \approx 394 \] Step 3: Calculate the percentage of female students in IIT Kanpur.
The number of female students in IIT Kanpur is 394, and the total number of students in IIT Kanpur is 945. To find the percentage of female students, we use the formula: \[ \text{Percentage of female students in IIT Kanpur} = \frac{394}{945} \times 100 \approx 41.67% \] Step 4: Conclusion.
Thus, the number of female students in IIT Kanpur is approximately 42% of the total number of students in it. Therefore, the correct answer is (D).