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ICSE Class X Math 2016 Paper

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Question : 50 of 57
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A bus covers a distance of 240 km240\text{ km} at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h10\text{ km}/\text{h} and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ' xx ' km/h\text{km}/\text{h}, form an equation and solve it to evaluate ' xx '.
Solution:  
Uniform speed=x km/h\text{Uniform speed}=x\text{ km}/\text{h}
distance=240 km\text{distance}=240\text{ km}
time=DistanceSpeed\text{time}=\frac{\text{Distance}}{\text{Speed}}
=240x hours=\frac{240}{x}\text{ hours}
Due to heavy rain speed =(x−10) km/h=(x-10)\text{ km}/\text{h}
Now time=240x−10 hours\text{time}=\frac{240}{x-10}\text{ hours}
According to question,
240x−10−240x=2\frac{240}{x-10}-\frac{240}{x}=2
240x−240(x−10)x(x−10)=2\frac{240x-240(x-10)}{x(x-10)}=2
240x−240x+2400x2−10x=2\frac{240x-240x+2400}{x^2-10x}=2
⇒2x2−20x−2400=0\Rightarrow 2 x^2-20x-2400=0
⇒x2−10x−1200=0\Rightarrow x^2-10x-1200=0
x2−40x+30x−1200=0x^2-40x+30x-1200=0
⇒(x−40)+30(x−40)=0\Rightarrow (x-40)+30(x-40)=0
⇒x−40)(x+30)=0\Rightarrow x-40)(x+30)=0
x=40 and x=−30x=40\text{ and }x=-30
(speed can not be negative)
∴\therefore uniform speed =40 km/h=40\text{ km}/\text{h}.
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