Direction: Answer the questions on the basis of the information given ...
Let the length of the Ganga Satluj Express be L1 m.
Speed of the Ganga Satluj Express
Let the length of the Shabd Bhedi Express be L2 m.
Speed of the Shabd Bhedi Express
Let the length of the Budhpurnima Express be L3 m.
Suppose the Ganga Satluj Express and the Budhpurnima Express meet after x hours. Then, Distance covered by Ganga Satluj Express + Distance covered by Budhpurnima Express = 232 km
Distance covered by Ganga Satluj Express
So distance covered by Budhpurnima Express = 100 m
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Direction: Answer the questions on the basis of the information given ...
Calculation of Speed and Time
To solve this question, we need to calculate the speeds and times of the Ganga Satluj Express and the Budhpurnima Express.
The Ganga Satluj Express crosses the 400 m long Malviya Bridge in 1 minute and 15 seconds. We can convert this time to seconds by multiplying 1 minute by 60 seconds and adding 15 seconds. So, the time taken by the Ganga Satluj Express to cross the bridge is 75 seconds.
Similarly, the Ganga Satluj Express crosses a fruit stall in 45 seconds.
The Budhpurnima Express runs at a speed of 50 km/hr. To convert this speed to m/s, we need to multiply it by 1000/3600, as there are 1000 meters in a kilometer and 3600 seconds in an hour. So, the speed of the Budhpurnima Express is 50 * (1000/3600) = 100/9 m/s.
The Shabd Bhedi Express travels at a speed of 25 m/s. It takes 30 seconds to cross the Ganga Satluj Express and 27 seconds to cross the Budhpurnima Express, both from the opposite direction.
Calculating Distances Covered
To find the distances covered by the Ganga Satluj Express and the Budhpurnima Express when they meet, we need to consider the time taken by each train to cover the respective distances.
Let's assume the distance covered by the Ganga Satluj Express when it meets the Budhpurnima Express is x meters.
The time taken by the Ganga Satluj Express to cross the fruit stall is 45 seconds. As the speed is distance/time, we can calculate the distance covered by the Ganga Satluj Express using the formula distance = speed * time. Therefore, the distance covered by the Ganga Satluj Express is (100/9) * 45 = 500 meters.
The time taken by the Budhpurnima Express to cover the distance between Gaya and Varanasi is given as 232 km. As the speed is distance/time, we can calculate the time taken by the Budhpurnima Express using the formula time = distance/speed. Therefore, the time taken by the Budhpurnima Express is (232 * 1000) / (50 * 1000/3600) = 13.92 hours.
Since the Budhpurnima Express starts 45 minutes later from Varanasi station, the time taken by the Ganga Satluj Express to cover the distance between Gaya and the meeting point is 13.92 hours - 45 minutes = 13.45 hours.
Now, we can calculate the distance covered by the Ganga Satluj Express using the formula distance = speed * time. Therefore, the distance covered by the Ganga Satluj Express is (25 * 3600) * 13.45 = 122,500 meters or 122.5 km.
Since the distance covered by the Ganga Satluj Express when it meets the Budhpurnima Express is x meters and the distance covered by the Ganga Satluj Express to cross the fruit stall is 500 meters, we can calculate the distance covered by the Ganga Satluj Express when it meets the Budhpurnima Express as x -
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