PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018
Answer
1260
Explanation
The total number of students in a school is always considered 100%. If boys are 75%, then the percentage of girls is (100% - 75%) = 25%. According to the question, 25% equals 420. Therefore, 1% equals (420/25) = 16.8. Hence, the number of boys (75%) is 16.8 × 75 = 1260.
Key Points
- > Total student percentage = 100%
- > Boys percentage = 75%
- > Girls percentage = 100% - 75% = 25%
- > 25% is equivalent to 420 students
- > 1% is equivalent to 420 ÷ 25 = 16.8
- > 75% is equivalent to 16.8 × 75 = 1260
- > Alternative method: The ratio of boys to girls is 75:25 or 3:1. So, boys = 420 × 3 = 1260.
Additional Information
Percentage and Ratio Relationships
| Fraction | Percentage | Ratio |
|---|---|---|
| Whole | 100% | 1/1 |
| Half | 50% | 1/2 |
| Quarter | 25% | 1/4 |
| Three-Quarters | 75% | 3/4 |
Memory Tips
- Shortcut Trick: If 25% = 420, then 75% is exactly 3 times of that. So, 420 × 3 = 1260.
- Golden Rule: Always assume the total quantity to be 100% in percentage-based word problems.