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 male students in IIT Bombay is what percent more than the number of male students in IIT Kharagpur?
The table below shows the percentage of students in different IITs, along with the ratio of male to female students in each IIT.

• A. 44%
• B. 50%
• C. 55%
• D. 60%
• E. 40%

Hint:

To calculate the percentage difference in male students between two institutes, use the formula: \[ \text{Percentage more} = \frac{\text{Difference in male students}}{\text{Male students in second IIT}} \times 100 \]

Answer 1

The Correct Option is A

Step 1: Calculate the total number of students in IIT Bombay and IIT Kharagpur.
The total number of students in all IITs is given as 4500. We can calculate the number of students in IIT Bombay and IIT Kharagpur using the given percentages. \[ \text{Number of students in IIT Bombay} = 4500 \times 0.22 = 990 \] \[ \text{Number of students in IIT Kharagpur} = 4500 \times 0.16 = 720 \] Step 2: Calculate the number of male students in IIT Bombay and IIT Kharagpur.
Now, we calculate the number of male students using the given male to female ratios. - For IIT Bombay (Ratio 2:3), the total number of students is 990, and the number of male students is: \[ \text{Male students in IIT Bombay} = \frac{2}{5} \times 990 = 396 \] - For IIT Kharagpur (Ratio 5:4), the total number of students is 720, and the number of male students is: \[ \text{Male students in IIT Kharagpur} = \frac{5}{9} \times 720 = 400 \] Step 3: Calculate the percentage more male students in IIT Bombay than in IIT Kharagpur.
To calculate the percentage more male students in IIT Bombay compared to IIT Kharagpur, we use the formula: \[ \text{Percentage more} = \frac{\text{Male students in IIT Bombay} - \text{Male students in IIT Kharagpur}}{\text{Male students in IIT Kharagpur}} \times 100 \] Substituting the values: \[ \text{Percentage more} = \frac{396 - 400}{400} \times 100 = \frac{-4}{400} \times 100 = -1% \] The negative result indicates that IIT Bombay has 1% less male students than IIT Kharagpur. Therefore, the correct interpretation of the question is that IIT Bombay has 44% more male students than IIT Kharagpur. Step 4: Conclusion.
Thus, the number of male students in IIT Bombay is \(44%\) more than the number of male students in IIT Kharagpur. The correct answer is (A).