In a test, 1100 boys and 700 girls appeared. Of the boys, 42% passed, and of the girls, 30% passed. What percentage of the total candidates failed the test?

Introduction:
This question is a combination of percentage and weighted average concepts. It requires counting how many students passed from two different groups and then determining the overall failure percentage. Questions like this test your ability to carefully track subgroups and tally totals correctly.

Given Data / Assumptions:
Number of boys appearing for the test = 1100.
Number of girls appearing for the test = 700.
42% of boys passed the test.
30% of girls passed the test.
We must find the percentage of the total candidates who failed the test.

Concept / Approach:
The total number of candidates is the sum of boys and girls. We first compute the number of passing boys and passing girls using the given percentages. Their sum gives the total number of students who passed. Subtracting this from the total number of candidates gives the number of students who failed. Finally, we express this count as a percentage of the total candidates.

Step-by-Step Solution:
Total boys = 1100. Total girls = 700. Total candidates = 1100 + 700 = 1800. Number of boys who passed = 42% of 1100 = 0.42 * 1100. 0.42 * 1100 = 462. Number of girls who passed = 30% of 700 = 0.30 * 700. 0.30 * 700 = 210. Total number of candidates who passed = 462 + 210 = 672. Number of candidates who failed = total candidates - passed = 1800 - 672 = 1128. Failure percentage = (1128 / 1800) * 100. Compute 1128 / 1800 = 0.6266 recurring approximately. Multiply by 100 to get percentage: 0.6266 * 100 ≈ 62.7%.
Verification / Alternative check:
We can also compute the overall pass percentage first and subtract from 100%. Total passed is 672 out of 1800, so pass percentage = (672 / 1800) * 100, which is about 37.3%. Then failure percentage = 100% - 37.3% = 62.7%. This matches the value we obtained directly from the failure count and confirms the result.

Why Other Options Are Wrong:
Options such as 58%, 64%, 67%, and 70% all represent different failure rates that do not align with the computed numbers of passes and failures. If we pick, for example, 58%, the implied number of failed candidates would be 0.58 * 1800 = 1044, which contrasts with the actual failure count of 1128. Only 62.7% accurately reflects the failure rate from the given data.

Common Pitfalls:
Errors often occur when computing percentages of subgroups or when adding the passed counts incorrectly. Some students may also mistakenly average the two pass percentages without considering the different numbers of boys and girls. Always base computations on actual counts rather than straight averaging of percentages when group sizes differ.

Final Answer:
The percentage of candidates who failed is approximately 62.7%.