Question : Aman decided to cover a distance of 12 km in 78 minutes. He decided to cover the initial two-thirds of the distance at 10 km/hr and the remaining at some different speed. Find the speed for the last one-third of the distance.
Option 1: 7.8 km/hr
Option 2: 8 km/hr
Option 3: 8.4 km/hr
Option 4: 9 km/hr
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Correct Answer: 8 km/hr
Solution : Time taken to cover a distance of 12 km = 78 minutes Two-thirds of the 12 km was covered at = 10 km/hr Time = $\frac{\text{Distance}}{\text{Speed}}$ Two thirds of $12$ km = $12\times{\frac{2}{3}}$ = 8 km Speed for 8 km distance cover = 10 km/hr So, Time = $\frac{8 }{10}$ = 0.8 h = 48 minutes ⇒ Time left = 78 – 48 = 30 minutes = $\frac{30}{60}$ = 0.5 hour Remaining distance = 12 – 8 = 4 km ⇒ Speed required for remaining 4 km = $\frac{4\mathrm{~km} }{0.5 \mathrm{~h}}$ = 8 km/hr So, the speed for the last one-third of the distance is 8 km/hr. Hence, the correct answer is 8 km/hr.
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