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A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 km away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is (a) 100 km/hr (b) 110 km/hr (c) 120 km/hr (d) 130 km/hr |
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Answer» (c) 120 km/hr Let the speed of the car be x km/hr Then, speed of the train = \(\frac{150x}{100}\) km/hr = \(\frac{3x}{2}\) km/hr Time taken by car to reach point B = \(\frac{75}{x}\) hrs Time taken by train to reach point B = \(\frac{75}{\frac{3}{2}x}\) hrs Given, \(\frac{75}{x}\) - \(\frac{75}{\frac{3}{2}x}\) = \(\frac{12.5}{60}\) ⇒ \(\frac{75}{x}\) - \(\frac{50}{x}\) = \(\frac{125}{10\times60}\) = \(\frac{5}{24}\) ⇒ \(\frac{25}{x}\) = \(\frac{5}{24}\) ⇒ x = \(\frac{25\times24}{5}\) = 120 km/hr. |
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