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 ✓ UPSC's answer
- (c) 182 cm
- (d) 210 cm
Why the answer is (b)
• A's net gain per chance is 6 cm - 1 cm = 5 cm, but on the 40th chance it reaches the top before slipping.
• So pillar X height = 39 × 5 cm + 6 cm = 195 cm + 6 cm = 201 cm.
• B's net gain per chance is 7 cm - 3 cm = 4 cm, with the 40th chance adding 7 cm.
• So pillar Y height = 39 × 4 cm + 7 cm = 156 cm + 7 cm = 163 cm.
• C's net gain per chance is 6.5 cm - 2 cm = 4.5 cm, with the 40th chance adding 6.5 cm.
• So pillar Z height = 39 × 4.5 cm + 6.5 cm = 175.5 cm + 6.5 cm = 182 cm; the shortest pillar is 163 cm, option (b).
Why the other options are wrong
- (a) 161 cm
- 161 cm is not the height of any of the three pillars, since X, Y and Z are 201 cm, 163 cm and 182 cm.
- (c) 182 cm
- 182 cm is the height of pillar Z, not the shortest pillar.
- (d) 210 cm
- 210 cm is not the height of any of the three pillars, since X, Y and Z are 201 cm, 163 cm and 182 cm.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.