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Class 10 › Mathematics › Quadratic Equations
CBSE2026Class Class 10 · Mathematics5 Marks · Long✅ Verified
(A) A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.
✅ Answer & Solution
Let the speed of the faster train be $x$ km/hr. Then speed of slower train $= (x-10)$ km/hr. Time taken by faster train $=\frac{200}{x}$ hr; time taken by slower train $=\frac{200}{x-10}$ hr. Given: $\frac{200}{x-10}-\frac{200}{x}=1$. $200\left[\frac{x-(x-10)}{x(x-10)}\right]=1$. $200\times\frac{10}{x(x-10)}=1$. $2000 = x^2-10x$. $x^2-10x-2000=0$. Using the quadratic formula: $x=\frac{10\pm\sqrt{100+8000}}{2}=\frac{10\pm\sqrt{8100}}{2}=\frac{10\pm90}{2}$. $x=50$ (rejecting negative value $x=-40$). Speed of faster train $=50$ km/hr; Speed of slower train $=50-10=40$ km/hr.
