UPSC Prelims 2016 · CSAT
Question 57: Basic Numeracy
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 :
AnswerUPSC’s answer is (b).
The broken part CB lies slanting from C, 12 m up the trunk, to the ground at D, 5 m from A. In right triangle ACD, CD = sqrt(12^2 + 5^2) = sqrt(169) = 13 m. The broken part equals CD, so the original height is AC + CB = 12 + 13 = 25 m. Remember the 5-12-13 triple.
Why each option is right or wrong
- (a) Would need a broken part of 8 m, but it is 13 m.
- (b) Right: 12 + 13 = 25 m.
- (c) Would need a broken part of 18 m.
- (d) Would need a broken part of 23 m.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.