CAPF AC 2022 Q31: General Mental Ability – Quantitative Aptitude
A number is 124 more than its one-third. What is that number?
- (a) 194
- (b) 180
- (c) 189
- (d) 186
Answer: (d) 186
Explanation
A number compared with its one-third
Given: a number is 124 more than its one-third; find the number.
How to think: if you take away one-third of a number, two-thirds is left.
So that two-thirds equals 124.
| Step | Working |
|---|---|
| Let the number be | x |
| Equation | x = x/3 + 124 |
| Bring x/3 across | x − x/3 = 124, so 2x/3 = 124 |
| One-third | x/3 = 62 |
| The number | x = 62 × 3 = 186 |
Check: one-third of 186 is 62, and 62 + 124 = 186.
Answer: (d) 186.
Why each option is right or wrong
- (a) Incorrect. 194 is not divisible by 3, and its one-third plus 124 is not 194.
- (b) Incorrect. One-third of 180 is 60, and 60 + 124 = 184, not 180.
- (c) Incorrect. One-third of 189 is 63, and 63 + 124 = 187, not 189.
- (d) CORRECT. Two-thirds of the number is 124, so the number is 186.
Key point
A number that is k more than its one-third: two-thirds of it equals k, so the number is 3k/2. Here 3 × 124 ÷ 2 = 186.
Remember
Two-thirds = 124, so the number = 186.
Common mistakes
- Multiplying 124 by 3 to get 372, forgetting that 124 is two-thirds, not one-third.
- Writing the equation as x/3 = x + 124, with the two sides swapped.
- Not checking the answer by putting it back into the statement.
Exam tip
Educated guess: 124 is two-thirds of the number, so the number is one and a half times 124. Half of 124 is 62, and 124 + 62 = 186.
Sources
- NCERT Class VII Mathematics — Simple Equations
- NCERT Class VIII Mathematics — Linear Equations in One Variable