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 problem describes a right-angled triangle formed by the remaining vertical trunk (AC), the ground distance (AD), and the broken part of the trunk (CB).
• The height of the remaining trunk AC is given as 12 meters.
• The distance from the base of the tree to where the top touches the ground, AD, is 5 meters.
• Using the Pythagorean theorem, the length of the broken part CB is calculated as the square root of (12^2 + 5^2), which is the square root of (144 + 25) = square root of 169 = 13 meters.
• The original height of the tree is the sum of the remaining vertical part (AC) and the broken part (CB), which is 12 + 13 = 25 meters.
• Therefore, the correct option is (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.