Anand travelled 300 km by train and 200 km by taxi. It took him 5 h and 30 min. However, if he travels 260 km by train and 240 km by taxi, he takes 6 min more. The speed of the train is
1st case :
Distance travelled by train = 300km and by taxi = 200km
Let the speed of train be x km/hr and that of taxi be y km/hr.
Time taken by train = 300/x and time taken by taxi = 200/y hr
$$\ \frac{\ 300}{x}$$Â = $$\ \frac{\ 200}{y}$$
Total time taken = 5hrs 30 mins = 5 1/2 hrs
$$\ \frac{\ 300}{x}$$ +$$\ \frac{\ 200}{y}$$= 5$$\ \frac{\ 1}{2}$$
On solving we get : 600y + 400x = 11xy ----- Eq (1)
2nd case :
Distance travelled by train = 260 km and by taxi = 240 km
The speed of train and taxi will remain the same.
Time taken by train = $$\ \frac{\ 260}{x}$$hr and by taxi = $$\ \frac{\ 240}{y}$$ hr
$$\ \frac{\ 260}{x}$$ + $$\ \frac{\ 240}{y}$$ = 5hrs 36 mins
$$\ \frac{\ 260}{x}$$ + $$\ \frac{\ 240}{y}$$ = 5$$\ \frac{\ 3}{5}$$ on solving we get,
1300y + 1200x = 28xy  ---- Eq (2)
Solving 1 and 2 we get:
x=100 km/hr
Speed of the train = 100km/hr
A is the correct answer.
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