Question : A person travels a distance of 240 km, partly by train and the rest by bus. He takes $3 \frac{1}{2}$ hours if he travels 150 km by train and the rest by bus. If he travels 140 km by bus and the rest by train, he takes $3 \frac{2}{3}$ hours. What is the speed of the train?
Option 1: 80 km/hr
Option 2: 70 km/hr
Option 3: 75 km/hr
Option 4: 72 km/hr
Correct Answer: 75 km/hr
Solution : Let the speed of the train be $x$ and the speed of the bus be $y$. According to the question, $\frac{150}{x} + \frac{90}{y} = \frac{7}{2}$ ⇒ $300y +180x = 7xy$......................................(1) Now, $\frac{140}{y} + \frac{100}{x} = \frac{11}{3}$ ⇒ $420x + 300y = 11xy$.....................................(2) Subtracting equation (1) from equation (2), we get ⇒ $240x = 4xy$ ⇒ $60 = y$ Speed of the bus = 60 km/hr From equation (1), $\frac{150}{x} + \frac{90}{60} = \frac{7}{2}$ ⇒ $\frac{150}{x} = \frac{7}{2}- \frac{3}{2}$ ⇒ $\frac{150}{x} = \frac{4}{2}$ ⇒ $x = 75$ Hence, the correct answer is 75 km/hr.
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Question : A bus travels at 100 km/hr for the first $\frac{1}{2}$ hour. Later it travels at 80 km/hr. Find the time taken by the bus to travel 290 km.
Option 1: 4 hours
Option 2: 3.5 hours
Option 3: 3 hours
Option 4: 2.5 hours
Question : The speeds of two trains are in the ratio 6 : 7. If the second train runs 364 km in 4 hours, then the speed of the first train is:
Option 1: 60 km/hr
Option 2: 72 km/hr
Option 3: 78 km/hr
Option 4: 84 km/hr
Question : A bus starts running with an initial speed of 33 km/hr and its speed increases every hour by a certain amount. If it takes 7 hours to cover a distance of 315 km, what will be the hourly increment (in km/hr) in the speed of the bus?
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
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 _____.
Option 1: $5 \frac{1}{4}$
Option 2: $5 \frac{1}{8}$
Option 3: $4 \frac{3}{7}$
Option 4: $4 \frac{5}{7}$
Question : A train covers a distance of 540 km between two stations in 240 minutes. It travels at a speed of 90 km/hr to another station in 5 hours. What is the average speed of the train (in km/hr)?
Option 1: 112
Option 2: 110
Option 3: 100
Option 4: 120
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