Madhya Pradesh Police Exam Model Paper 3

Given data :
Distance between Pune to Mumbai (D) = 200 km
Speed of A (A) – Speed of B (B) = 20 km/hr
Meeting time while travelling towards each other = 2 hours
Speed of C (C) = (B + 10) km/hr
Formula used :
Speed = Distance/time
Relative speed A and B (moving towards each other) = (Speed)A + (Speed)B
Calculation :
Let, speed of B = x km/hr
Speed of $\mathit{A}=\left(\mathit{x}+20\right)$ km/hr
The relative speed of A and B while travelling towards each other = A + B
$\Rightarrow \mathit{x}+\mathit{x}+20$
$\Rightarrow \left(2\mathit{x}+20\right)$ km/hr
Relative Time to cover distance = Distance/(Relativetime)
$\Rightarrow 2=200/\left(2\mathit{x}+20\right)$
$\Rightarrow 2\times \left(2\mathit{x}+20\right)=200$
$\Rightarrow 4\mathit{x}+40=200$
$\Rightarrow 4\mathit{x}=16$ 0
$\Rightarrow \mathit{x}=40$ km/hr
⇒ Speed of $\mathit{A}=\mathit{x}+20=40+20=60$ km/hr
⇒ Speed of $\mathit{B}=\mathit{x}=40$ km/hr
⇒ Speed of $\mathit{C}=\mathit{B}+10$
$\Rightarrow 40+10=50$ km/hr
Time required for C to travel from Pune to Mumbai = Distance/Speed
$\Rightarrow 200/50=4$ hours
∴ C will take 4 hours for travelling from Pune to Mumbai.