भिन्न ऊँचाइयों के तीन खम्भे X, Y और Z हैं। तीन मकड़ियाँ A, B और C क्रमशः इन खम्भों पर एक ही समय पर चढ़ना शुरू करती हैं। एक प्रयास में A, X पर 6 cm चढ़ती है किन्तु 1 cm नीचे फिसल जाती है। B, Y पर 7 cm चढ़ती है किन्तु 3 cm नीचे फिसल जाती है। C, Z पर 6·5 cm चढ़ती है किन्तु 2 cm नीचे फिसल जाती है। यदि उनमें से प्रत्येक मकड़ी को खम्भे के शीर्ष तक पहुँचने के लिए 40 प्रयास करना पड़ता है, तो सबसे छोटे खम्भे की ऊँचाई क्या है?
Read this question in English
There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?
(a) 161 cm · (b) 163 cm · (c) 182 cm · (d) 210 cm
उत्तर और व्याख्या · explanation in English
Answer: (b) 163 cm
A spider does not slip back in the chance in which it reaches the top, so height = 39 net gains + one full climb. That gives X = 201 cm, Y = 163 cm and Z = 182 cm; the shortest pillar is 163 cm.
- Net gain per chance: A = 6 − 1 = 5 cm, B = 7 − 3 = 4 cm, C = 6.5 − 2 = 4.5 cm.
- In the 40th chance each spider reaches the top and does not slip, so height = 39 × (net gain) + (full climb).
- X = 39 × 5 + 6 = 201 cm; Y = 39 × 4 + 7 = 163 cm; Z = 39 × 4.5 + 6.5 = 182 cm.
- Shortest pillar = 163 cm (Y).
- Check for Y: after 38 chances B is at 152 cm and reaches only 159 cm in the 39th climb, so it truly needs the 40th.
Remember · Climb-and-slip problems: the last climb has no slip. Height = (n − 1) × net gain + one full climb.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·