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?

The correct option is 163 cm.

Let's analyze the movement of each spider step-by-step to calculate the heights of the three pillars X, Y, and Z.

Spider A on Pillar X:

- In each of the initial chances, Spider A climbs 6 cm and slips down 1 cm.

- Net progress per chance (except the last one) = $6-1=5$ cm.

- On the final 40th chance, once Spider A reaches the top after climbing 6 cm, it does not slip down.

- Therefore, for the first $39$ chances, net progress = $39\times 5=195$ cm.

- On the 40th chance, it climbs 6 cm to reach the top.

- Height of Pillar X = $195+6=201$ cm.

Spider B on Pillar Y:

- In each of the initial chances, Spider B climbs 7 cm and slips down 3 cm.

- Net progress per chance (except the last one) = $7-3=4$ cm.

- For the first $39$ chances, net progress = $39\times 4=156$ cm.

- On the 40th chance, it climbs 7 cm to reach the top.

- Height of Pillar Y = $156+7=163$ cm.

Spider C on Pillar Z:

- In each of the initial chances, Spider C climbs 6.5 cm and slips down 2 cm.

- Net progress per chance (except the last one) = $6.5-2=4.5$ cm.

- For the first $39$ chances, net progress = $39\times 4.5=175.5$ cm.

- On the 40th chance, it climbs 6.5 cm to reach the top.

- Height of Pillar Z = $175.5+6.5=182$ cm.

Comparing the heights of the three pillars:

- Height of Pillar X = 201 cm

- Height of Pillar Y = 163 cm

- Height of Pillar Z = 182 cm

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