Question : Two trains, A and B, start from stations X and Y and travel towards Y and X, respectively. After passing each other, they take 4 hours 48 minutes, and 3 hours 20 minutes respectively to reach Y and X. If train A is moving at 45 km/hr, then the speed of train B is:
Option 1: 60 km/hr
Option 2: 64.8 km/hr
Option 3: 54 km/hr
Option 4: 37.5 km/hr
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Correct Answer: 54 km/hr
Solution : Given: Two trains, A and B, start from stations X and Y and travel towards Y and X, respectively. After passing each other, they take 4 hours 48 minutes, and 3 hours 20 minutes, respectively, to reach Y and X and train A is moving at 45 km/hr. Let the speed of train B be $x$ km/hr. The speed of train A is 45 km/hr. Time taken by train A = 4 hours 48 minutes = $\frac{24}{5}$ hours. Time taken by train B = 3 hours 20 minutes = $\frac{10}{3}$ hours. According to the question, $\frac{45}{x}=\sqrt{\frac{\frac{10}{3}}{\frac{24}{5}}}$ ⇒ $\frac{45}{x}=\sqrt{\frac{25}{36}}$ ⇒ $\frac{45}{x}=\frac{5}{6}$ ⇒ $x=\frac{45×6}{5}=54$ So, the speed of train B is 54 km/hr. Hence, the correct answer is 54 km/hr.
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Question : Two stations R and S are 400 km apart from each other. A train leaves from R to S and simultaneously another train leaves from S to R. Both trains meet after 10 hours. If the speed of the first train is 4 km/hr more than the second train, then what is the speed of the slower train?
Option 1: 18 km/hr
Option 2: 26 km/hr
Option 3: 16 km/hr
Option 4: 22 km/hr
Question : A and B start moving from places X to Y and Y to X, respectively, at the same time on the same day. After crossing each other, A and B take $5 \frac{4}{9}$ hours and 9 hours, respectively, to reach their respective destinations. If the speed of A is 33 km/hr, then the speed (in km/hr) of B is:
Option 1: 22
Option 2: 2
Option 3: $25 \frac{2}{3}$
Option 4: $24 \frac{1}{3}$
Question : X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/hr and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
Option 1: 2 : 3
Option 2: 1 : 3
Option 3: 2 : 4
Option 4: 1 : 4
Question : A moving train passes a 50-metre-long platform in 14 seconds and a lamp post in 10 seconds. The speed of the train (in km/hr) is:
Option 1: 24 km/hr
Option 2: 36 km/hr
Option 3: 40 km/hr
Option 4: 45 km/hr
Question : A person travels in a car at 40 km/hr for 3 hours, on a bike at 30 km/hr for 2 hours, and in a train at 80 km/hr for 5 hours. What is the average speed at which he travelled?
Option 1: 56 km/hr
Option 2: 60 km/hr
Option 3: 62 km/hr
Option 4: 58 km/hr
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