CAPF AC 2021 Q98: General Mental Ability – Quantitative Aptitude
If 35% of a number is 416 more than 27% of the same number, then the number is
- (a) 5200
- (b) 2600
- (c) 3900
- (d) 3328
Answer: (a) 5200
Explanation
Finding a number from a percentage difference
Given: 35% of a number is 416 more than 27% of the same number; find the number.
How to think: both percentages are of the same number.
So simply subtract them.
| Step | Working |
|---|---|
| Difference of percentages | 35% − 27% = 8% |
| 8% of the number | 416 |
| 1% of the number | 416 ÷ 8 = 52 |
| The number | 52 × 100 = 5200 |
Check: 35% of 5200 is 1820 and 27% of 5200 is 1404.
1820 − 1404 = 416.
Answer: (a) 5200.
Why each option is right or wrong
- (a) CORRECT. 8% of the number is 416, so the number is 5200.
- (b) Incorrect. 8% of 2600 is only 208.
- (c) Incorrect. 8% of 3900 is only 312, not 416.
- (d) Incorrect. 3328 is 416 × 8, a wrong operation; 8% of it is about 266.
Key point
a% of N − b% of N = (a − b)% of N. Find 1% first, then multiply by 100.
Remember
Same number: subtract the percentages first.
Common mistakes
- Multiplying 416 by 8 instead of dividing by 8 to find 1%.
- Adding the two percentages (62%) instead of subtracting them.
- Forgetting to multiply by 100 after finding 1% of the number.
Exam tip
Educated guess: 8% is about one-twelfth. Twelve times 416 is about 5000, so 5200 is the only option near it.
Sources
- NCERT Class VII Mathematics — Comparing Quantities (percentage)
- R. S. Aggarwal, Quantitative Aptitude — Percentage