In a city there are 4,800 engineers in total. The number of female engineers is 3/8 of the total number of engineers. The number of female engineers is what percentage of the number of male engineers?

Introduction / Context:
This problem combines fractions and percentages in a demographic context. We are given the fraction of female engineers out of a total and asked to express the number of female engineers as a percentage of the number of male engineers. Such questions appear in data interpretation and percentage sections and help strengthen understanding of relative comparison between two groups.

Given Data / Assumptions:

• Total number of engineers = 4800.
• Female engineers are 3/8 of the total.
• Male engineers are the remaining engineers after counting females.
• We must find female engineers as a percentage of male engineers.

Concept / Approach:
First, we use the fraction 3/8 to find the exact number of female engineers. Then we subtract this from the total to get the number of male engineers. Once we have both counts, we compute the percentage using the formula: Percentage = (Number of females / Number of males) * 100. It is important to note that we are not asked for the percentage of females out of the total, but specifically out of the male count.

Step-by-Step Solution:
Step 1: Total engineers = 4800. Step 2: Female engineers = (3 / 8) * 4800. Step 3: Compute (3 / 8) * 4800 = 3 * 600 = 1800. Step 4: Male engineers = Total - Female = 4800 - 1800 = 3000. Step 5: We need female engineers as a percentage of male engineers. Step 6: Percentage = (Number of females / Number of males) * 100. Step 7: Substitute values: Percentage = (1800 / 3000) * 100. Step 8: 1800 / 3000 = 0.6, and 0.6 * 100 = 60%. Step 9: So, the number of female engineers is 60% of the number of male engineers.

Verification / Alternative check:
We can reduce the ratio of female to male engineers first. Females : Males = 1800 : 3000. Divide both by 300 to get 6 : 10. This ratio says for every 10 male engineers there are 6 female engineers. To convert 6 out of 10 to a percentage, compute (6 / 10) * 100 = 60%. This matches the earlier result, confirming the calculation.

Why Other Options Are Wrong:
76%, 56%, 52%, and 48% do not correspond to the ratio 1800 : 3000. For instance, 56% would imply a female to male ratio of 56 : 100, which is less than the actual 6 : 10, and 76% would imply a much higher ratio. Only 60% agrees with the simplified ratio 6 : 10. Therefore, the other options are inconsistent with the given data.

Common Pitfalls:
A common mistake is to compute the percentage of females out of the total (which would be 37.5%) rather than out of the male population. Another pitfall is miscalculating the fraction 3/8 of 4800 or forgetting to subtract from the total to find the male count. Carefully tracking what base quantity the percentage is relative to is crucial for correct answers in such questions.

Final Answer:
The number of female engineers is 60% of the number of male engineers.