Multiple choice

Find the value of Q1 and Q2 and state the correct relationship. Quantity I: Time taken by A to complete 1/5th of work if B takes 6 days to complete 3/5th of work and together they take 5 days to complete 3/4th of work Quantity II: Time taken by a train to cross a platform of length 60 km given that it crosses a pole in two and a half hours running at 60 km/hr

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Quantity I: B takes 6 days for 3/5 work, so B's rate = (3/5)/6 = 1/10 per day. B takes 10 days alone. A + B together take 5 days for 3/4 work, so combined rate = (3/4)/5 = 3/20 per day. A's rate = 3/20 - 1/10 = 1/20 per day. A takes 20 days alone. For 1/5 work: time = (1/5)/(1/20) = 20/5 = 4 days. Quantity II: Train crosses a pole (its own length) in 2.5 hours at 60 km/hr. So train length = 60 × 2.5 = 150 km. Wait - that's very long for a train. Let me reconsider: crossing time = length/speed, so length = speed × time = 60 × 2.5 = 150 km. To cross a 60 km platform: distance = 150 + 60 = 210 km. Time = 210/60 = 3.5 hours. Comparing: Quantity I = 4 days, Quantity II = 3.5 hours. 4 days > 3.5 hours, so Quantity I is greater.

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