A cyclist covering a distance of 40 km would have reached 1 hour earlier if he had run at an increased speed of 2 km/hr His speed in (km/hr) was

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Solution

The correct option is B 8
Let the speed of the cyclist be x km/hr $∴ \frac{40}{x} - \frac{40}{x + 2} = 1 \Rightarrow \frac{40 (x + 2) - 40 x}{x (x + 2)} = 1$
$\Rightarrow 80 = x^{2} + 2 x \Rightarrow x^{2} + 2 x - 80 = 0$
$\Rightarrow x^{2} + 10 x - 8 x - 80 = 0$
$\Rightarrow x (x + 10) - 8 (x + 10) = 0$
$\Rightarrow (x - 8) (x + 10) = 0 \Rightarrow x = 8 o r - 10$
Neglecting -ve values, we take x = 8 km/hr

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A cyclist covering a distance of 40 km would have reached 1 hour earlier if he had run at an increased speed of 2 km/hr His speed in (km/hr) was

The correct option is B 8Let the speed of the cyclist be x km/hr ∴40x−40x+2=1⇒40(x+2)−40xx(x+2)=1⇒80=x2+2x⇒x2+2x−80=0⇒x2+10x−8x−80=0⇒x(x+10)−8(x+10)=0⇒(x−8)(x+10)=0⇒x=8or−10Neglecting -ve values, we take x = 8 km/hr