In a college, the number of boys is 75% of the number of girls, and the difference between the numbers of girls and boys is 35. On a particular day, 20% of the boys are absent. How many boys are present in the college on that day?

Introduction / Context:
This question combines percentage and difference relationships between two groups, boys and girls, with an absence scenario. The goal is to determine the actual number of boys present on a particular day using given percentage based ratios and a fixed numerical difference. This structure is very typical in aptitude problems involving school or college populations.

Given Data / Assumptions:

Number of boys is 75% of the number of girls.

Difference between the numbers of girls and boys is 35.

On a particular day, 20% of the boys are absent.

We need to find the number of boys present on that day.

Concept / Approach:
First, translate the 75% relationship into an equation between boys (B) and girls (G). Then use the given difference G − B = 35 to solve for B and G. After finding the total number of boys, compute 20% absent and subtract that from the total to obtain the number of boys present. This uses both algebra and percentage calculations in a straightforward way.

Step-by-Step Solution:
Step 1: Let number of girls be G and number of boys be B.Step 2: Boys are 75% of girls, so B = 75% of G = (75 / 100) * G = (3 / 4) * G.Step 3: The difference between girls and boys is 35: G − B = 35.Step 4: Substitute B = (3 / 4) * G into this equation: G − (3 / 4) * G = 35.Step 5: Simplify: (1 − 3 / 4) * G = (1 / 4) * G = 35.Step 6: Hence G = 35 * 4 = 140.Step 7: Boys B = (3 / 4) * 140 = 105.Step 8: On the particular day, 20% of the boys are absent.Absent boys = 20% of 105 = (20 / 100) * 105 = 21.Step 9: Boys present = total boys − absent boys = 105 − 21 = 84.

Verification / Alternative check:
Check the values: girls = 140, boys = 105. Boys are 105 / 140 = 0.75 = 75% of girls and the difference is 140 − 105 = 35, exactly as given. On the given day, 20% of 105 equals 21 absent, leaving 84 present. Everything is consistent with the problem statement.

Why Other Options Are Wrong:
72, 93, 81, and 70 do not result from the correct combination of the ratio, the difference of 35, and the 20% absence calculation. They either correspond to wrong intermediate values or incorrect application of the percentage step.

Common Pitfalls:
Some students may reverse the 75% relationship and mistakenly set G = 75% of B. Others lose track of whether the 20% is taken of boys or total students. Another frequent mistake is to use the difference 35 directly as 25% of some value without properly setting up equations. Always define variables clearly and translate every relationship systematically into algebraic form before solving.

Final Answer:
The number of boys present in the college on that day is 84.