2018 · Q58
Two pillars are placed vertically 8 feet apart. The height difference of the two pillars is 6 feet. The two ends of a rope of length 15 feet are tied to the tips of the two pillars. The portion of the length of the taller pillar that can be brought in contact with the rope without detaching the rope from the pillars is
general-mental-abilityquantitative-aptitude
- Aless than 6 feet
- Bmore than 6 feet but less than 7 feet
- Cmore than 7 feet but less than 8 feet
- Dmore than 8 feet
Explanation
If a length y of the rope lies along the taller pillar, the remaining 15−y must span the 8 ft horizontal gap and the reduced vertical gap of (6−y) ft. Setting √(8² + (6−y)²) = 15−y and squaring gives 100 − 12y = 225 − 30y, so y = 125/18 ≈ 6.94 ft. That is more than 6 feet but less than 7 feet. Hence option B.