UPSC Prelims 2017·CSAT·Quantitative Aptitude·Arithmetic

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?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. A161
  2. B163Correct
  3. C182
  4. D210

Explanation

Here's a brief explanation:

  1. Calculate net climb per chance for each spider:

    • Spider A: 6 cm up - 1 cm down = 5 cm net climb.
    • Spider B: 7 cm up - 3 cm down = 4 cm net climb.
    • Spider C: 6.5 cm up - 2 cm down = 4.5 cm net climb.

  2. Understand the "last chance" logic: For the first 39 chances, the spider experiences the net climb and slip. In the 40th (last) chance, the spider makes its final climb and reaches the top without slipping down.

  3. Calculate the height of each pillar:

    • Pillar X (Spider A): (39 chances * 5 cm/chance) + 6 cm (final climb) = 195 + 6 = 201 cm.
    • Pillar Y (Spider B): (39 chances * 4 cm/chance) + 7 cm (final climb) = 156 + 7 = 163 cm.
    • Pillar Z (Spider C): (39 chances * 4.5 cm/chance) + 6.5 cm (final climb) = 175.5 + 6.5 = 182 cm.

  4. Compare the heights:

    • Pillar X = 201 cm
    • Pillar Y = 163 cm
    • Pillar Z = 182 cm

  5. The shortest pillar is Y, with a height of 163 cm.

Therefore, option B is correct.

Quantitative Aptitude: There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simult
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