Question : P and Q are 27 km away. Two trains with speeds of 24 km/h and 18 km/h, respectively, start simultaneously from P and Q and travel in the same direction. They meet at a point R, beyond Q. Distance QR is:
Option 1: 126 km
Option 2: 81 km
Option 3: 48 km
Option 4: 36 km
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Correct Answer: 81 km
Solution : Given: P and Q are 27 km away. Two trains start simultaneously from P and Q and travel in the same direction at 24 km/h and 18 km/h, respectively. Formula: The relative speed is the difference in speeds of the two trains. Time = $\frac{\text{Relative distance}}{\text{Relative speed}}$ Distance = Speed × Time Solution: Relative speed = 24 – 18 = 6 km/h Time required by the faster train to overtake the slower train = $\frac{27}{6}$ = 4$\frac{1}{2}$ hours $\therefore$ Distance between Q and R = Distance travelled by slower train = 18 × 4$\frac{1}{2}$ hr = 81 km Hence, the correct answer is 81 km.
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