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      Question

      Two cyclists P and Q are at towns A and B. P sets off

      toward B at (x – 8) km/h. Two hours later, Q starts toward A at (x + 8) km/h. They meet at the exact halfway point between A and B. If AB = 240 km, find P’s time to go from A to B.
      A 18 hrs Correct Answer Incorrect Answer
      B 20 hrs Correct Answer Incorrect Answer
      C 12 hrs Correct Answer Incorrect Answer
      D 10 hrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Distance covered by P in 2 hours = (x – 8) × 2 = 2(x – 8) km Remaining distance = 240 – 2(x – 8) = 240 – 2x + 16 = (256 – 2x) km Time of meet after Q starts = (256 – 2x)/(2x) hours According to question, [(256 – 2x)/(2x)] × (x + 8) = 240/2 (256x + 2048 – 2x² – 16x) = 240x ⇒ –2x² + 2048 = 0 x² = 1024 x = 32 Speed of P = 32 – 8 = 24 km/h Therefore, required time = 240/24 = 10 hours

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