ICSE Class X Math 2016 Solved Paper

Question : 50

Total: 57

A bus covers a distance of 240‌km at a uniform speed. Due to heavy rain its speed gets reduced by 10‌km∕h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ' x ' km∕h, form an equation and solve it to evaluate ' x '.

Solution:

‌ Uniform speed ‌‌=x‌km∕h
‌ distance ‌‌=240‌km
‌ time ‌‌=‌

‌ Distance ‌

‌ Speed ‌

‌=‌

240

‌ hours ‌
Due to heavy rain speed =(x−10)‌km∕h
Now ‌ time ‌=‌

240

x−10

‌ hours ‌
According to question,
‌

240

x−10

−‌

240

‌=2
‌

240x−240(x−10)

x(x−10)

‌=2
‌‌

240x−240x+2400

x2−10x

‌=2
⇒2x2−20x−2400‌=0
⇒x2−10x−1200‌=0
x2−40x+30x−1200‌=0
⇒(x−40)+30(x−40)‌=0
⇒x−40)(x+30)‌=0
x=40‌ and ‌x‌=−30
(speed can not be negative)
∴‌‌ uniform speed =40‌km∕h.

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