Two iron balls weigh 3.5 kg and 7.5 kg respectively. What is the weight of the first ball expressed as a percentage of the weight of the second ball?

Introduction / Context:
This question tests your ability to express one quantity as a percentage of another. Such problems involving weights, lengths, or amounts are common in everyday life and in examinations, and the method is always the same: use the basic percentage formula with the correct base value.

Given Data / Assumptions:
Weight of first iron ball = 3.5 kg. Weight of second iron ball = 7.5 kg. We must express the weight of the first ball as a percentage of the second ball.

Concept / Approach:
To find A as a percentage of B, we use the formula percent = (A / B) * 100. Here A is the weight of the first ball, and B is the weight of the second ball. After computing the percentage, we may convert it into a mixed fraction if needed, as in 46 2/3 percent.

Step-by-Step Solution:
Let A = 3.5 kg and B = 7.5 kg. Required percent = (A / B) * 100. Compute A / B = 3.5 / 7.5. Write 3.5 as 35/10 and 7.5 as 75/10, so the ratio becomes (35/10) / (75/10) = 35 / 75. Simplify 35 / 75 by dividing numerator and denominator by 5 to get 7 / 15. Now multiply by 100: (7 / 15) * 100. Compute 700 / 15 = 46.6666 repeating. So percentage = 46.6666 repeating percent, which is 46 2/3 percent.

Verification / Alternative check:
We can check by converting 46 2/3 percent back to a decimal. Write 46 2/3 as 46.6666 repeating and divide by 100 to get 0.466666 repeating. Multiply 7.5 by 0.466666 repeating and we get approximately 3.5, confirming that the calculation is consistent.

Why Other Options Are Wrong:
Options 35 percent and 45 percent underestimate the ratio since 3.5 is nearly half of 7.5. Fifty percent would correspond to exactly half, but 3.5 is slightly less than half of 7.5. The value 46 1/3 percent is slightly lower than the actual ratio, while 46 2/3 percent is the exact ratio obtained from 700 divided by 15.

Common Pitfalls:
Learners can mistakenly compute 7.5 as a percentage of 3.5 instead of the other way around, or they may round intermediate steps too early and get a slightly off mixed fraction. Another possible confusion is forgetting to multiply by 100 when converting a fraction to percentage. Staying systematic with the formula avoids these issues.

Final Answer:
The weight of the first iron ball is 46 2/3 percent of the weight of the second ball.