CAPF AC 2025 Q59: General Mental Ability – Quantitative Aptitude
- (a) a
- (b) 2a
- (c) 3a
- (d) 4a
Answer: (b) 2a
Explanation
Two trees and a point on the ground
Given: P is on the ground, on the same line as the bases and the tips of trees A and B, to the left of both.
Heights of A and B are in the ratio 1 : 3, and the distance PA = a metres.
How to think: the line from P through both tips is a straight line, so the two right triangles (P to A's base and tip, P to B's base and tip) are similar.
Their heights are in the ratio 1 : 3, so their distances from P are also in the ratio 1 : 3.
| Step | Working | Result |
|---|---|---|
| Ratio of distances | PA : PB = 1 : 3 | PB = 3a |
| Distance between the trees | AB = PB − PA = 3a − a | 2a |
Bank key corrected: the stored key was (c) 3a; the right answer is (b) 2a.
Answer: (b) 2a.
Why each option is right or wrong
- (a) Incorrect. a is the distance from P to the first tree, not the gap between the trees.
- (b) CORRECT. PB = 3a, so AB = 3a − a = 2a.
- (c) Incorrect. 3a is the distance from P to the second tree, not between the trees.
- (d) Incorrect. 4a does not follow from the 1 : 3 ratio.
Key point
Similar triangles: heights 1 : 3 gives distances from P also 1 : 3. PB = 3a, AB = PB − PA = 2a.
Remember
Same ratio of heights and distances from P: PB = 3a, AB = 2a.
Common mistakes
- Giving PB (3a) as the answer instead of subtracting PA.
- Adding the distances, 3a + a, which gives 4a.
- Forgetting that the tips lie on a straight line through P.
Exam tip
Educated guess: if P is a, and the second tree is three times as far, the gap between them is 3a − a. Options a and 3a are the 'wrong distances' and 4a is the sum.
Sources
- NCERT Class X Mathematics, Chapter 6 (Triangles: similarity and basic proportionality)
- NCERT Class VIII Mathematics, Chapter 13 (Direct and Inverse Proportions)