Question : A train travels at a speed of 18 m/s in the first 5 minutes, covers 7.5 km in the next 10 minutes and covers 12 km in another 10 minutes. What is its average speed (in km/h, rounded off to 1 decimal place) for the entire journey?
Option 1: 59.8
Option 2: 71.2
Option 3: 45.7
Option 4: 64.6
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Correct Answer: 59.8
Solution : Speed of train in the first 5 minutes = 18 m/s Distance travelled by train in next 10 mins = 7.5 km Distance travelled by train in next 10 mins = 12 km Distance = Speed $\times$ Time Distance travelled by train in the first 5 mins = $18\times (5\times 60)$ = 5400 m = 5.4 km Total time taken = $\frac{5}{60} + \frac{10}{60} + \frac{10}{60} = \frac{25}{60} = \frac{5}{12}$ hr Average Speed = $\frac{\text{Total distance}}{\text{Total time taken}}$ $= \frac{(5.4 + 7.5 + 12)\times 12}{5} = \frac{24.9\times 12}{5}=\frac{298.8}{5} = 59.8$ km/hr Hence, the correct answer is 59.8.
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