Question
Three individuals—Aman,
Bittu, and Raju—each complete a distance of 120 meters in different time durations: 'x' seconds for Aman, 'x - 2' seconds for Bittu, and 'x + 3' seconds for Raju. Additionally, the ratio of Aman's speed to Raju's speed is given as 5:4. Quantity I: If Bittu and Raju compete in a 300-meter race, how much distance will separate them when the winner crosses the finish line? Quantity II: If Aman and Raju compete in a 320-meter race, how much distance will separate them when the winner crosses the finish line? In the question, two quantities i.e. Quantity I and Quantity II are given. Solve the given quantities to establish the correct relation between them and choose the correct option.Solution
ATQ, 120 = 5 × x = 4 × (x + 3) 5x = 4x + 12 x = 12 Speed of Aman = 120/12 = 10 m/s Speed of Bittu = 120/(12 - 2) = 120/10 = 12 m/s Speed of Raju = 120/(12 + 3) = 120/15 = 8 m/s Quantity I, Distance between Bittu & Raju, when winner finish the race = 300 - 300/12 × 8 = 300 - 200 = 100 m Quantity II, Distance between Bittu & Raju, when winner finish the race = 320 - 320/10 × 8 = 320 - 256 = 64 m Quantity I > Quantity II
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