CAPF AC 2023 Q80: General Mental Ability – Data Interpretation
The next three items are based on a survey on the occurrence of vowels in a certain book, irrespective of whether they are in upper or lower case:
| Vowel | A | E | I | O | U |
|---|---|---|---|---|---|
| Percentage | 20 | 45 | 15 | 8 | 12 |
If "O" and "U", irrespective of upper or lower case, occur exactly 5040 times, then how many times does the letter "E" occur in the book in the upper or the lower case?
- (a) 11840
- (b) 11600
- (c) 11430
- (d) 11340
Answer: (d) 11340
Explanation
Finding E from O and U
How to think: turn the percentages into a ratio.
You do not need the total number of vowels.
Data: the survey gives the percentage occurrence of each vowel in a certain book, irrespective of whether it is in upper or lower case.
A = 20, E = 45, I = 15, O = 8, U = 12.
| Step | Working |
|---|---|
| O and U together | 8 + 12 = 20% |
| 20% equals | 5040 |
| 1% equals | 5040 / 20 = 252 |
| E is 45% | 252 × 45 = 11340 |
Multiplying 252 × 45 quickly:
| Part | Value |
|---|---|
| 252 × 40 | 10080 |
| 252 × 5 | 1260 |
| Total | 11340 |
Educated guess: 252 × 45 must end in 0 and be a multiple of 9.
The digits of 11340 add to 9, so only that option fits.
Answer: (d) 11340.
Why each option is right or wrong
- (a) Incorrect. 11840 is not 252 × 45; its digits add to 14, so it is not a multiple of 9.
- (b) Incorrect. 11600 is not a multiple of 9, while 252 × 45 must be.
- (c) Incorrect. 11430 is a multiple of 9 but comes from swapping the digits of 11340.
- (d) CORRECT. 1% is 252, so E at 45% occurs 11340 times.
Key point
O + U = 20% = 5040, so 1% = 252. E = 45% = 252 × 45 = 11340.
Remember
20% = 5040, so 45% = 11340.
Common mistakes
- Using only O (8%) or only U (12%) for 5040 instead of both together.
- Finding the total (25200) and stopping there.
- Swapping digits while multiplying and marking 11430.
Exam tip
Unitary method: find 1% first, then multiply by what is asked.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (percentages)
- Arun Sharma — How to Prepare for Data Interpretation for the CAT (Tata McGraw-Hill)