Question : When Alisha goes by car at 50 km/hr, she reaches her office 5 minutes late. But when she took her motorbike, she reached 3 minutes early. If her office is 25 km away, what is the approximate average speed at which she rides her motorbike?
Option 1: 68 km/hr
Option 2: 62 km/hr
Option 3: 58 km/hr
Option 4: 52 km/hr
Correct Answer: 68 km/hr
Solution : The speed at which Alisha drives her car = 50 km/hr The distance that Alisha has to travel to reach her office = 25 km Also, the difference between the time taken by her to reach the office by bike and car = 8 minutes = $\frac{2}{15}$ hr Let the speed of the bike be $x$ km/hr. So, $\frac{25}{50}-\frac{25}{x}=\frac{2}{15}$ $⇒\frac{25}{x}=\frac{1}{2}-\frac{2}{15}$ $\therefore x=25\times \frac{30}{11}=\frac{750}{11}=68.18\approx 68$ km/hr Hence, the correct answer is 68 km/hr.
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