Question : A bus can travel 20% faster than a scooter. Both start from point P at the same time and reach point Q, 60 km away from point P, at the same time. On the way, however, the bus lost about 10 minutes while stopping at bus stations, while the scooter did not stop anywhere. What is the speed of the bus?
Option 1: 68 km/hr
Option 2: 80 km/hr
Option 3: 60 km/hr
Option 4: 72 km/hr
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Correct Answer: 72 km/hr
Solution : Given: A bus can travel 20% faster than a scooter. Let the scooter's speed be $x$ km/hr So, the speed of the bus = $1.2x$ km/hr Use the formula, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$ According to the question, $\frac{60}{x}–\frac{60}{1.2x}=\frac{10}{60}$ ⇒ $\frac{7.2–6}{1.2x}=\frac{1}{60}$ ⇒ $\frac{1.2}{1.2x}=\frac{1}{60}$ ⇒ $x=60$ km/hr The speed of the bus = $1.2x=1.2\times 60=72$ km/hr Hence, the correct answer is 72 km/hr.
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Question : A car left 4 hours later than the scheduled time but in order to reach its destination 480 km away in time, it had to increase its usual speed by 10 km/hr. What is the usual speed of the car?
Option 1: 40 km/hr
Option 2: 60 km/hr
Option 3: 30 km/hr
Option 4: 50 km/hr
Question : A person walks 10 km at a speed of 2.5 km/hr, then runs 10 km at a speed of 5 km/hr and then goes 30 km by bus at the speed of 30 km/hr. What is the average speed of the man?
Option 1: 9 km/hr
Option 2: 8.25 km/hr
Option 3: 7.14 km/hr
Option 4: 7 km/hr
Question : A girl, walking at $\frac{5}{6}$ of her usual speed, misses the bus by 7 minutes. How long does it usually take to reach the bus stop?
Option 1: 24 minutes
Option 2: 35 minutes
Option 3: 30 minutes
Option 4: 60 minutes
Question : An auto-rickshaw travels 20 km from point P to Q and then 25 km from Q to R. The total time taken was 1 hour 30 minutes. What was the average speed of the auto-rickshaw?
Option 1: 15 km/hr
Option 2: 30 km/hr
Option 3: 45 km/hr
Option 4: 60 km/hr
Question : A bus travels 60 km in the first hour, 40 km in the second hour and 50 km in the third hour. What is the average speed of the bus?
Option 1: 60 km/hr
Option 2: 45 km/hr
Option 3: 50 km/hr
Option 4: 55 km/hr
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