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      Question

      Find the distance travelled by car A in 3hrs 45 min if

      it is given that speed of car A is 4 km/h less than that of car B and time taken by car B to travel 80 km is 30 min less than time taken by car A to cover a distance of 90 km.
      A 135 km Correct Answer Incorrect Answer
      B 105 km Correct Answer Incorrect Answer
      C 125 km Correct Answer Incorrect Answer
      D 115 km Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Let speed of car B is ‘x’ km/h Speed of car A = ‘x – 4’ km/h So, 90/(x – 4) – 80/x = 1/2 => (90x – 80x + 320)/{x(x – 4)} = 1/2 => x2 – 4x = 20x + 640 => x2 – 24x – 640 = 0 => x2 – 40x + 16x – 640 = 0 => x(x – 40) + 16(x – 40) = 0 => (x + 16)(x – 40) = 0 => x = 40 Speed of car A = 40 – 4 = 36 km/h Desired distance = 36 × 3.75 = 135 km

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