CAPF AC 2025 Q70: General Mental Ability – Quantitative Aptitude
The value at the tenth place of a three-digit number is twice the value at the unit's place. The value at the hundredth place is 75% of the value at the unit's place. How many such numbers are possible?
- (a) 0
- (b) 1
- (c) 2
- (d) 3
Answer: (b) 1
Explanation
Digits of a three-digit number
Given: the tens digit is twice the units digit; the hundreds digit is 75% of the units digit.
How to think: let the units digit be u.
Then tens = 2u and hundreds = 0.75u = 3u/4.
All three must be whole digits from 0 to 9, so u must be a multiple of 4, and 2u must be at most 9.
| u | Tens (2u) | Hundreds (3u/4) | Valid number? |
|---|---|---|---|
| 0 | 0 | 0 | No, not a three-digit number |
| 4 | 8 | 3 | Yes: 384 |
| 8 | 16 | 6 | No, 16 is not a digit |
Only one number, 384, is possible.
Answer: (b) 1.
Why each option is right or wrong
- (a) Incorrect. The number 384 satisfies both conditions.
- (b) CORRECT. 384 is the only such number.
- (c) Incorrect. u = 8 fails because the tens digit would be 16.
- (d) Incorrect. Only u = 4 gives valid digits.
Key point
Digits: hundreds = 3u/4, tens = 2u, units = u. u must be a multiple of 4 with 2u ≤ 9, so u = 4: the number is 384.
Remember
Units 4, tens 8, hundreds 3: the single number 384.
Common mistakes
- Counting u = 8 as valid although the tens digit becomes 16.
- Counting u = 0, which does not give a three-digit number.
- Reading 75% as 0.75 of the number, not of the units digit.
Exam tip
Educated guess: 75% means 3/4, so the units digit is a multiple of 4. Only 4 and 8 qualify and 8 breaks the tens digit rule.
Sources
- NCERT Class VI Mathematics, Chapter 3 (Playing with Numbers: digits and place value)
- NCERT Class VIII Mathematics, Chapter 16 (Playing with Numbers: numbers in generalised form)