10. At a cricket match between Mumbai Indians (MI) and Chennai Super Kings (CSK), 28% of the
spectators are young while the rest are old. If 65% of the spectators are fans of CSK, and 25% of the
CSK fans are young, then the percentage of old people among the MI fans is nearest to
a. 66
b. 55
c. 62
d. 59
Percentage of Old People Among MI Fans
Problem Breakdown
The percentage of old people among MI fans is nearest to 66%.
Assume 100 total spectators for simplicity.
- Total spectators = 100
- Young spectators = 28 → Old spectators = 72
- CSK fans = 65 → Young CSK fans = 25% of 65 = 16.25 → Old CSK fans = 48.75
- MI fans = 35 → Young MI fans = 28 − 16.25 = 11.75 → Old MI fans = 35 − 11.75 = 23.25
Therefore, the percentage of old people among MI fans is calculated as:
(23.25 / 35) × 100 ≈ 66.43%
Hence, approximately 66% of MI fans are old people.
Option Analysis
Comparing each option against the calculated 66.43%:
| Option | Percentage | Nearest to 66.43%? | Explanation |
|---|---|---|---|
| a. 66 | 66% | Yes | Matches closest (difference of 0.43%), correct choice for “nearest to”. |
| b. 55 | 55% | No | Underestimates by ~11%, ignores the high old spectator proportion (72%) driving old MI fans higher. |
| c. 62 | 62% | No | Underestimates by ~4%, possibly from miscalculating young MI fans or overlap between teams. |
| d. 59 | 59% | No | Farthest underestimate (~7%), likely assumes uniform age distribution across teams. |
Exam Strategy
Such problems test conditional percentages and cross-category relationships common in CSIR NET quantitative aptitude sections.
To verify, check totals:
- Young total (28) = Young CSK (16.25) + Young MI (11.75)
- Old MI (23.25) fits perfectly.
A quick formula validation:
Old MI% = (72 − 48.75) / 35 × 100 = 66.43%
Practicing such shortcuts helps eliminate distractors efficiently in competitive exams.
