In a college there are 1650 students and the difference between the number of boys and the number of girls is 400; what is the percentage of girls in the college?

Introduction / Context:
This question is a straightforward application of solving simultaneous equations and then converting the result into a percentage. It involves a group of students separated into boys and girls with a known total and a known difference. These types of problems are very common in aptitude tests and help in practicing basic algebra and percentage conversion.

Given Data / Assumptions:

• Total number of students in the college = 1650.
• The difference between the number of boys and the number of girls is 400.
• We assume the number of boys is greater than the number of girls, which is natural because the difference is stated without sign.
• We are asked for the percentage of girls in the college.

Concept / Approach:
Let the number of boys be B and the number of girls be G. We know B + G equals the total students and B - G equals the given difference. Solving these two linear equations gives us B and G. After that, the percentage of girls is (G / total) * 100. This approach is standard for all such total and difference type questions that appear in exams.

Step-by-Step Solution:
Let the number of boys be B and the number of girls be G.We are given B + G = 1650.We are also given B - G = 400.Add the two equations: (B + G) + (B - G) = 1650 + 400.This gives 2B = 2050, so B = 2050 / 2 = 1025.Substitute B = 1025 into B + G = 1650 to find G.So 1025 + G = 1650 implies G = 1650 - 1025 = 625.Percentage of girls = (G / total) * 100 = (625 / 1650) * 100.Compute 625 / 1650 which is approximately 0.3788, so percentage is about 37.88%.Rounded to the nearest whole percent, this is 38%.

Verification / Alternative check:
Check the numbers with the original conditions. Boys = 1025, girls = 625. The total is 1025 + 625 = 1650, which matches the given total students. The difference is 1025 - 625 = 400, which matches the stated difference. The percentage of girls is 625 divided by 1650, multiplied by 100, giving close to 37.88%. In exam options, we choose the nearest value, which is 38%, confirming our calculation.

Why Other Options Are Wrong:
49% would mean girls are roughly 808, but that would give a different difference between boys and girls from the given 400.

34% and 43% correspond to different student counts for girls and cannot satisfy both the total and the difference equations simultaneously.

Common Pitfalls:
Some candidates directly assume boys are 1025 and girls are 625 by guesswork or miscalculate the division when converting to percentage. Others might mistakenly compute the percentage of boys instead of girls or mix up the total and difference equations. Writing equations clearly and solving step by step, followed by a quick check of totals and differences, is the best way to avoid errors.

Final Answer:
The percentage of girls in the college is approximately 38%.