2023 · Q96
In a desert, X and Y are two spots that are separated by 100 km. At point X, are placed two pillars, one black and one white. On joining X and Y, a white pillar is placed every 180 km and a black pillar is placed every 350 km. How many times can one find both black and white pillars together while traveling from X to Y?
General Mental Ability, Quantitative Aptitude and StatisticsTime, work and measurement
- A16
- B14
- C15
- D17
Explanation
White pillars occur every 180 m and black pillars every 350 m, so both coincide at multiples of LCM(180, 350) = 6300 m = 6.3 km. Along the 100 km stretch from X to Y, coincidences occur at 6.3, 12.6, ..., 94.5 km, i.e., floor(100/6.3) = 15 times en route (the pair placed at X itself is the starting point). Hence (c) '15' is correct.