Question : Sudhin cycled at 8.5 km/hr for 4 hours, then took an auto and travelled at 20 km/hr for 1.5 hours and then walked at 4 km/hr for y hours. If Sudhin's overall average speed for the entire journey was 10 km/hr, what is the value of y?
Option 1: 2
Option 2: 1.25
Option 3: 1.5
Option 4: 1.75
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Correct Answer: 1.5
Solution :
Distance travelled by Sudhin cycling at 8.5 km/h for 4 hours = 8.5 × 4 = 34 km
Distance travelled by Sudhin in an auto at 20 km/h for 1.5 hours = 20 × 1.5 = 30 km
Distance travelled by Sudhin walking at 4 km/h for y hours = 4 × y = 4y km
Total time taken = (4 + 1.5 + y) = (5.5 + y) hours
Average speed = $\frac{\text{Total distance travelled}}{\text{Total time}}$
⇒ $10 = \frac{34 + 30 + 4y}{5.5 + y}$
⇒ $55 + 10y = 64 + 4y$
$\therefore y = \frac{3}{2}=1.5$
Hence, the correct answer is 1.5.
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