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A train covers 400 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 2 hours less for the same journey. What is the speed of the train (in km/h)?1. 252. 353. 304. 40 |
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Answer» Correct Answer - Option 4 : 40 Given: Distance = 400 km Let speed be x km/hr When speed is increase (x + 10) km/hr Formula Used: Distance = Speed × Time Calculation: According to question, ⇒ {(400/x) - (400/x +10)} = 2 hours ⇒ 400{(1/x) - (1/x + 10)} = 2 ⇒ {(1/x) - (1/x + 10)} = 2/400 ⇒ \(\frac{{10}}{{{x^{2\;}} + 10x}}\)= 1/200 ⇒ \({x^2}\) + 10x - 2000 = 0 ⇒ \({x^2}\) + 50x - 40x - 2000 = 0 ⇒ x(x + 50) - 40(x + 50) ⇒ (x + 50) (x - 40) = 0 ⇒ x = 40, -50 But , Speed can not be negative. ∴ Speed is 40 km/hr |
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