Multiple choice

P and Q are 27 km away. Two trains with speeds of 24 km/hr and 18 km/hr, respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is

  1. 48 km

  2. 36 km

  3. 126 km

  4. 81 km
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D Correct answer
Explanation

Relative speed = 24 - 18 = 6 km/hr. Distance between them = 27 km. Time to meet = 27 / 6 = 4.5 hours. Distance QR = speed of Q * time = 18 * 4.5 = 81 km.

AI explanation

Since the trains travel in the same direction, we use relative speed, which is the difference between their speeds: 24 km/hr minus 18 km/hr equals 6 km/hr. The faster train must cover the initial gap of 27 km to catch up to the slower train, which takes 27 km divided by 6 km/hr, or 4.5 hours. In this time, the slower train travels from Q at a speed of 18 km/hr for 4.5 hours. The distance QR is 18 multiplied by 4.5, which gives 81 km.

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