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(A) Let the speed of the train be $x\, km/h$ and the time taken be $t\, hours$. The distance $d$ is given by $d = xt$ $...(i)$.According to the first

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$600$

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(A) Let the speed of the train be $x\, km/h$ and the time taken be $t\, hours$. The distance $d$ is given by $d = xt$ $...(i)$.According to the first condition,if the speed is $(x + 10)\, km/h$,the time taken is $(t - 2)\, hours$:$(x + 10)(t - 2) = d$$xt - 2x + 10t - 20 = d$Since $d = xt$,we get $-2x + 10t = 20$,or $-x + 5t = 10$ $...(ii)$.According to the second condition,if the speed is $(x - 10)\, km/h$,the time taken is $(t + 3)\, hours$:$(x - 10)(t + 3) = d$$xt + 3x - 10t - 30 = d$Since $d = xt$,we get $3x - 10t = 30$ $...(iii)$.Multiplying equation $(ii)$ by $2$,we get $-2x + 10t = 20$ $...(iv)$.Adding $(iii)$ and $(iv)$:$(3x - 10t) + (-2x + 10t) = 30 + 20$$x = 50\, km/h$.Substituting $x = 50$ in equation $(ii)$:$-50 + 5t = 10$$5t = 60$$t = 12\, hours$.Distance $d = xt = 50 	imes 12 = 600\, km$.

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