CAPF AC 2021 Q77: General Mental Ability – Quantitative Aptitude
The average age of Raj and his father is 45 years. If the ages of the father and the grandfather of Raj are respectively two and three times that of Raj, then the age of Raj's grandfather is
- (a) 75 years
- (b) 90 years
- (c) 81 years
- (d) 84 years
Answer: (b) 90 years
Explanation
Ages of three generations
Given: the average age of Raj and his father is 45 years; the father is two times and the grandfather three times as old as Raj; find the grandfather's age.
How to think: let Raj's age be x.
The average tells you the sum of two ages.
| Step | Working |
|---|---|
| Let | Raj = x, father = 2x, grandfather = 3x |
| Sum of Raj and father | 45 × 2 = 90 |
| Equation | x + 2x = 90 |
| Raj | x = 30 years |
| Grandfather | 3 × 30 = 90 years |
Check: Raj 30 and father 60 give an average of 45.
Answer: (b) 90 years.
Why each option is right or wrong
- (a) Incorrect. 75 years would make Raj 25 and the average 37.5 years.
- (b) CORRECT. Raj is 30, so the grandfather is 3 × 30 = 90 years.
- (c) Incorrect. 81 years would make Raj 27 and the average 40.5 years.
- (d) Incorrect. 84 years would make Raj 28 and the average 42 years.
Key point
Average × number of items = sum. Use one variable for the smallest age and express the others as multiples.
Remember
Average 45 of two = sum 90.
Common mistakes
- Treating 45 as the sum of the two ages instead of the average.
- Including the grandfather in the average, though it covers only Raj and his father.
- Giving the father's age (60) when the question asks for the grandfather's.
Exam tip
Educated guess: the grandfather is three times Raj and the father is twice Raj. The sum of Raj and father is also three times Raj, which is 90. So the grandfather's age equals that sum.
Sources
- NCERT Class VII Mathematics — Simple Equations and Data Handling (arithmetic mean)
- R. S. Aggarwal, Quantitative Aptitude — Problems on Ages