ICSE Class X Math 2016 Solved Paper

Question : 50 of 57

Marks: +1, -0

A bus covers a distance of

240 {\km}

at a uniform speed. Due to heavy rain its speed gets reduced by

10 {\km} \/ {\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:

\;\text " Uniform speed "\;\;=x {\km} \/ {\h}

\;\text " distance "\;\;=240 {\km}

\;\text " time "\;\;=\;{\;\text " Distance "\;}/{\;\text " Speed "\;}

\;=\;{240}/{x} \;\text " hours "\;

Due to heavy rain speed

=(x-10) {\km} \/ {\h}

Now

\;\text " time "\;=\;{240}/{x-10} \;\text " hours "\;

According to question,

\;{240}/{x-10}-\;{240}/{x}\;=2

\;{240 x-240(x-10)}/{x(x-10)}\;=2

\;\;{240 x-240 x+2400}/{x^2-10 x}\;=2

⇒ 2 x^2-20 x-2400\;=0

⇒ x^2-10 x-1200\;=0

x^2-40 x+30 x-1200\;=0

⇒(x-40)+30(x-40)\;=0

⇒ x-40)(x+30)\;=0

x=40 \;\text " and "\; x\;=-30

(speed can not be negative)

∴ \;\;

uniform speed

=40 {\km} \/ {\h}

Go to Question:

Prev Question

Next Question