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A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?
- a)72 km/h
- b)66 km/h
- c)69 km/h
- d)75 km/h
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A train crossed a 110 m long platform in 13.5 seconds and a 205 m long...
Let the length of train be xm.
⇒ Speed of train = (length of platform + length of train )/ time
According to question,
⇒ (110+x)/13.5 = (205+x)/18.25
⇒ (110+x)/2.7 = (205+x)/3.65
⇒ 401.5+3.65� = 553.5+2.7x
⇒ 0.95x = 152
⇒ x = 160
⇒ Speed of train = (110 + 160)/13.5 = 20m/sec = 20m/sec = 20 x (18/5) = 72 km/hr
⇒ Speed of train = (length of platform + length of train )/ time
According to question,
⇒ (110+x)/13.5 = (205+x)/18.25
⇒ (110+x)/2.7 = (205+x)/3.65
⇒ 401.5+3.65� = 553.5+2.7x
⇒ 0.95x = 152
⇒ x = 160
⇒ Speed of train = (110 + 160)/13.5 = 20m/sec = 20m/sec = 20 x (18/5) = 72 km/hr
Most Upvoted Answer
A train crossed a 110 m long platform in 13.5 seconds and a 205 m long...
To find the speed of the train, we need to calculate the distance covered by the train in both cases and divide it by the time taken.
Let's assume the speed of the train is 'v' m/s.
Case 1:
The train crosses a 110 m long platform in 13.5 seconds.
- Distance covered by the train = length of the train + length of the platform = 110 m + 110 m = 220 m
- Time taken = 13.5 seconds
Using the formula speed = distance/time, we can calculate the speed of the train in this case:
Speed = 220 m / 13.5 s = 16.3 m/s
Case 2:
The train crosses a 205 m long platform in 18.25 seconds.
- Distance covered by the train = length of the train + length of the platform = 205 m + 205 m = 410 m
- Time taken = 18.25 seconds
Using the formula speed = distance/time, we can calculate the speed of the train in this case:
Speed = 410 m / 18.25 s = 22.4 m/s
Now, we have two values for the speed of the train in different cases.
To find the average speed of the train, we can take the average of these two speeds:
Average speed = (16.3 m/s + 22.4 m/s) / 2 = 19.35 m/s
But the answer options are in km/h, so let's convert the average speed from m/s to km/h:
1 m/s = 3.6 km/h
Average speed = 19.35 m/s * 3.6 km/h = 69.66 km/h
Rounded to the nearest whole number, the speed of the train is 70 km/h.
Since none of the answer options match 70 km/h, we can conclude that the given options are incorrect. However, the closest option to the calculated speed is option 'A' which is 72 km/h.
Let's assume the speed of the train is 'v' m/s.
Case 1:
The train crosses a 110 m long platform in 13.5 seconds.
- Distance covered by the train = length of the train + length of the platform = 110 m + 110 m = 220 m
- Time taken = 13.5 seconds
Using the formula speed = distance/time, we can calculate the speed of the train in this case:
Speed = 220 m / 13.5 s = 16.3 m/s
Case 2:
The train crosses a 205 m long platform in 18.25 seconds.
- Distance covered by the train = length of the train + length of the platform = 205 m + 205 m = 410 m
- Time taken = 18.25 seconds
Using the formula speed = distance/time, we can calculate the speed of the train in this case:
Speed = 410 m / 18.25 s = 22.4 m/s
Now, we have two values for the speed of the train in different cases.
To find the average speed of the train, we can take the average of these two speeds:
Average speed = (16.3 m/s + 22.4 m/s) / 2 = 19.35 m/s
But the answer options are in km/h, so let's convert the average speed from m/s to km/h:
1 m/s = 3.6 km/h
Average speed = 19.35 m/s * 3.6 km/h = 69.66 km/h
Rounded to the nearest whole number, the speed of the train is 70 km/h.
Since none of the answer options match 70 km/h, we can conclude that the given options are incorrect. However, the closest option to the calculated speed is option 'A' which is 72 km/h.
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A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?a)72 km/hb)66 km/hc)69 km/hd)75 km/hCorrect answer is option 'A'. Can you explain this answer?
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