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(B) Let the usual speed of the train be $x\, km/hr$.Time taken to cover $400\, km$ at usual speed is $T_1 = \frac{400}{x}$ hours.When the speed is dec

Vedclass · Accepted Answer

$25\, km/hr$

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(B) Let the usual speed of the train be $x\, km/hr$.Time taken to cover $400\, km$ at usual speed is $T_1 = \frac{400}{x}$ hours.When the speed is decreased by $5\, km/hr$,the new speed is $(x - 5)\, km/hr$.Time taken at the new speed is $T_2 = \frac{400}{x - 5}$ hours.According to the problem,$T_2 - T_1 = 4$.So,$\frac{400}{x - 5} - \frac{400}{x} = 4$.Dividing by $4$,we get $\frac{100}{x - 5} - \frac{100}{x} = 1$.$100x - 100(x - 5) = x(x - 5)$.$100x - 100x + 500 = x^2 - 5x$.$x^2 - 5x - 500 = 0$.$(x - 25)(x + 20) = 0$.Since speed cannot be negative,$x = 25\, km/hr$.

When there is a decrease of $5\, km/hr$ in the usual uniform speed of a train,it takes $4$ hours more than the usual time for covering the distance of $400\, km$. Find the usual speed of the train.

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