In an examination, 65% of the candidates passed. If the number of failures was 420, find the total number of examinees.
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: 1200
Explanation
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:
T = 420 / 0.35.0.35 = 7/20 ⇒ T = 420 * (20/7).420/7 = 60; 60 * 20 = 1200.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:
1200