Three spiders A, B and C start to climb on three pillars X, Y and Z of different heights 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
▶ Answer & Explanation
Correct answer: B. 163 cm
Spider A makes a net progress of 5 cm per chance (6 cm up - 1 cm down). Spider B makes a net progress of 4 cm per chance (7 cm up - 3 cm down). Spider C makes a net progress of 4.5 cm per chance (6.5 cm up - 2 cm down). Each spider takes 40 chances to reach the top. Thus, the heights of the pillars are 5 cm/chance * 40 chances = 200 cm for X, 4 cm/chance * 40 chances = 160 cm for Y, and 4.5 cm/chance * 40 chances = 180 cm for Z. However, the final climb in the last chance does not involve slipping. So, the height for B would be 39*4 + 7 = 156 + 7 = 163 cm. Similarly for A: 39*5 + 6 = 195 + 6 = 201 cm. For C: 39*4.5 + 6.5 = 175.5 + 6.5 = 182 cm. Comparing 201 cm, 163 cm, and 182 cm, the shortest pillar is 163 cm.
Source: UPSC csat 2017