Question : A student goes to school at the rate of $\frac{5}{2}$ km/hr and reaches 6 minutes late. If he travels at the speed of 3 km/hr, he reaches 10 minutes earlier. The distance from the school is:
Option 1: 45 km
Option 2: 20 km
Option 3: 10 km
Option 4: 4 km
Correct Answer: 4 km
Solution : Let the distance from the school be $x$ km. According to the question, $\frac{x}{\frac{5}{2}}-\frac{x}{3}=\frac{6+10}{60}$ ⇒ $\frac{2x}{5}-\frac{x}{3}=\frac{16}{60}$ ⇒ $6x-5x=\frac{16}{60}×15$ $\therefore x=4$ km Hence, the correct answer is 4 km.
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Question : If Abhi travels a certain distance at 6 km/hr, he reaches his destination 12 minutes early, but if he travels at 4 km/hr, he reaches his destination 10 minutes late. The speed (in km/hr) at which he should travel to reach his destination on time is _____.
Question : A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/hr speed and 10 minutes earlier if he walks at a speed of 4 km/hr. The distance he has to walk is:
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