AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is :
- (a) 20 m
- (b) 25 m ✓ UPSC's answer
- (c) 30 m
- (d) 35 m
Why the answer is (b)
• The standing part AC (12 m), the ground distance AD (5 m) and the broken part CD form a right-angled triangle with the right angle at A.
• CD² = 12² + 5² = 144 + 25 = 169, so the broken part is 13 m long.
• Original height = standing part + broken part = 12 + 13 = 25 m.
• Hence 25 m, option (b).
Why the other options are wrong
- (a) 20 m
- Option (a) is incorrect because 20 meters does not equal the sum of the vertical segment (12 m) and the hypotenuse (13 m).
- (c) 30 m
- Option (c) is incorrect because 30 meters is not the result of adding the vertical height (12 m) and the broken length (13 m).
- (d) 35 m
- Option (d) is incorrect because 35 meters is not the result of adding the vertical height (12 m) and the broken length (13 m).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.