A train can travel 40% faster than a car. Both the train and car start from point A at the same time and reach point B, which is 70 kms away from A, at the same time. On the way, however, the train lost about 15 minutes while stopping at stations. The speed of the train in km/h is:
Let the speed of the car be x.Â
Then the speed of the train be x + 40% of x.
i.e; (x +Â $$\frac{40}{100}\times\ x$$) = 1.4x
Time taken by train to cover the distance of 70 km :Â Â
i.e;Â $$\frac{70}{1.4x}$$
Time taken by car to cover the distance of 70 km :Â
i.e;Â $$\frac{70}{x}$$
According to question,Â
$$\frac{70}{x}-\frac{70}{1.4x}=\frac{15}{60}$$
$$\therefore\ \frac{98-70}{1.4x}=\frac{15}{60}$$
$$\therefore\ \frac{28}{1.4x}=\frac{15}{60}$$
$$\therefore\ 21x=1680$$
$$\therefore\ x=80$$
So, Speed of Train = 1.4x =Â $$1.4\times\ 80=112\ \frac{km}{hr}$$
Hence, Option C is correct.Â
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