Question : Anand covered a certain distance in the first leg lasting 5 hours, at the speed of 50 km/hr. In the second leg, he increased his speed by 20% due to which he covered 20% more distance than in the first leg. He covered the third leg at the average speed of the first two legs and covered 10% more distance than in the second leg. How much time (in hours) did he take to complete all three legs?
Option 1: 16
Option 2: 15
Option 3: 18
Option 4: 14
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Correct Answer: 16
Solution :
Anand took 5 hours for the first leg, at 50 km/hr speed.
He covered a distance of 5 × 50 = 250 km
Then, he increased his speed by 20%.
New speed = $50 + \frac{20}{100} \times 50$ = 60 km/hr
New distance = $250 + \frac{20}{100} \times 250$ = 300 km
Time taken = $\frac{300}{60}$ = 5 hours
For the third leg, his speed = $\frac{(50 + 60)}{2}$ = 55 km/hr
Distance covered = $300 + \frac{10}{100}\times300$ = 330 km
Time taken = $\frac{330}{55}$ = 6 hours
$\therefore$ Total time taken = 5 + 5 + 6 = 16 hours
Hence, the correct answer is 16 hours.
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