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 6cm 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 the requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?

Correct Option (2)

To determine the height of each pillar, the net distance covered by each spider per chance must be calculated. Since each spider reaches the top in the 40th chance, it implies that in the final chance, the spider covers its full climb distance without slipping, as it has already reached the apex.

• Spider A (Pillar X):
  • Net climb per chance = 6 cm (climb) - 1 cm (slip) = 5 cm.
  • Distance covered in 39 chances = 39 × 5 cm = 195 cm.
  • Total height of Pillar X = 195 cm + 6 cm (40th chance climb) = 201 cm.
• Spider B (Pillar Y):
  • Net climb per chance = 7 cm (climb) - 3 cm (slip) = 4 cm.
  • Distance covered in 39 chances = 39 × 4 cm = 156 cm.
  • Total height of Pillar Y = 156 cm + 7 cm (40th chance climb) = 163 cm.
• Spider C (Pillar Z):
  • Net climb per chance = 6.5 cm (climb) - 2 cm (slip) = 4.5 cm.
  • Distance covered in 39 chances = 39 × 4.5 cm = 175.5 cm.
  • Total height of Pillar Z = 175.5 cm + 6.5 cm (40th chance climb) = 182 cm.

Comparing the calculated heights: Pillar X = 201 cm, Pillar Y = 163 cm, Pillar Z = 182 cm. The shortest pillar is Pillar Y, with a height of 163 cm.

Incorrect Options:

• Option 1 (161 cm): This value does not correspond to the calculated height of any of the pillars.
• Option 3 (182 cm): This is the height of Pillar Z, which is not the shortest among the three pillars.
• Option 4 (210 cm): This value does not correspond to the calculated height of any of the pillars.