In an examination, 65% of the candidates passed. If the number of failures was 420, find the total number of examinees.

Introduction / Context:
Pass percentage and number of failures combine to determine the total candidates. If 65% passed, then 35% failed. Given the count of failures, we scale up to the total population.

Given Data / Assumptions:

• Pass rate = 65% → Fail rate = 35%.
• Failures = 420 candidates.

Concept / Approach:
If Total = T, then 0.35T = 420 ⇒ T = 420 / 0.35. Using fraction 35% = 7/20 makes mental math straightforward: T = 420 ÷ (7/20) = 420 * (20/7).

Step-by-Step Solution:

Verification / Alternative check:
Compute 65% of 1200 = 780 pass; 35% of 1200 = 420 fail, matching the given failure count.

Why Other Options Are Wrong:

• 567, 693, 1000: These totals do not yield exactly 420 failures at 35%.

Common Pitfalls:
Confusing pass and fail percentages, or dividing by 65 rather than 0.65/0.35. The failures correspond to 35% of the total.

Final Answer: