Question

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Answer 1

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$let \: the \: speed \: of \: fast \: train \: = x \: km \: hr \: \\ let \: the \: speed \: of \: slow \: train \: = (x - 10)km \: hr \\ distance \: covered \: by \: fast \: trai n \: = 200km \\ \\ now \: \: acc.to \: ques. \: \\ \frac{200}{x} = \frac{200}{x - 10} - 1 \\ = > \frac{200}{x} = \frac{200 - (x - 10)}{x - 10} \\ = > 200(x - 10) = 200x - {x}^{2} + 10x \\ = > 200x - 2000 = 200x - {x}^{2} + 10x \\ = > - 2000 = - {x}^{2} + 10x \\ = > - 2000 + {x}^{2} - 10x \\ = > {x}^{2} - 50x + 40x - 2000 = 0 \\ = > x(x - 50) + 40(x - 50) = 0 \\ = > (x - 50)(x +40) = 0 \\ = > x = 50 \: \: and \: \: x = - 40 \\ \\ so \: speed \: of \: fast \: train \: = 50 \: km \: hr \\ speed \: of \: slower \: train = 40km \: hr$
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