Mathematics · Time, Speed and Distance

Analyze the text and evaluate the three quantities: Quantity I: A cyclist and a truck travel the same distance S. The ratio of their speeds is 7:5. The cyclist takes 36 minutes less than the truck. If the truck starts with a lead of (S-35) km, the cyclist overtakes it in 14 hours. Find the speed of the cyclist in km/hr. Quantity II: Priya travels from Pune and Anand from Hyderabad (distance = 480 km) towards each other with speeds in the ratio 3:4. If Priya increases her speed by 12 km/hr, they meet at a point 76 times farther from Pune than their original meeting point. Determine Anand's speed in km/hr. Quantity III: Metro-X and Metro-Y move at speeds in the ratio 4:5. The ratio of times taken to cross a lamp post is 3:4. Moving towards each other, they cross completely in 329 seconds. Metro-Y takes 8 seconds to pass a 250m platform. Find the speed of Metro-X in km/hr.