Question

In covering a distance of 30km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is:
A. 5 kmph
B. 7 kmph
C. 6.25 kmph
D. 7.5 kmph

Answer 1

- Hint: Assume time taken by Sameer to cover 30km be “t”. Calculate speed of Sameer and Abhay by using the formula,
$\text{Speed = }\dfrac{\text{Distance travelled}}{\text{time taken}}...........\left( 1 \right)$

Complete step-by-step solution -

Let the time taken by Sameer to cover a distance of 30km be “t” hours.
Hence,
$\begin{align}
  & \text{Speed of Sameer = }\dfrac{\text{Distance travelled}}{\text{time taken}} \\
 & \therefore \ \text{Speed of Sameer = }\left( \dfrac{30}{t} \right)km/hour \\
\end{align}$
According to the question, Abhay takes 2 hours more than Sameer.
Hence, the time taken by Abhay to cover a distance of 30km = (t +2) hours.
Hence,
$\begin{align}
  & \text{Speed of Abhay = }\dfrac{\text{Distance travelled}}{\text{time taken}} \\
 & \therefore \ \text{Speed of Abhay = }\left( \dfrac{30}{t+2} \right)km/hour.........\left( 2 \right) \\
\end{align}$
Now, when Abhay doubles his speed, then he would take 1 hour less than Sameer.
$\begin{align}
  & \text{New speed of Abhay = 2}\times \text{ previous speed of Abhay} \\
 & \text{ =2}\times \text{ }\left( \dfrac{30}{t+2} \right)km/hour.........\left( 3 \right) \\
\end{align}$
Total time taken by Abhay to cover 30km with new speed,
\[\begin{align}
  & =\dfrac{\text{Distance travelled}}{\text{New speed of Abhay}} \\
 & \text{= }\dfrac{30\left( t+2 \right)}{2\times 30}\ \ \ \ \ \ \ \ \left( \text{using equation }\left( 3 \right) \right) \\
 & =\dfrac{t+2}{2}hours \\
\end{align}\]
Given that, this time taken by Abhay is equal to 1 hour less than time taken by Sameer.
$\Rightarrow \left( \dfrac{t+2}{2} \right)=\left( t-1 \right)$
  $\text{since, time taken by sameer } $
  $\text{is equal to ''t'' hours} $
 $\Rightarrow t+2=2\left( t-1 \right) $
  $\Rightarrow t+2=2t-2 $
  $\Rightarrow 2+2=2t-t $
  $\Rightarrow 4=t $
$\therefore $ “t” is equal to 4 hours.
From equation (1), speed of Abhay $=\dfrac{30}{t+2}km/hr$
Putting the values of t = 4 hours, we get speed of Abhay,
$\begin{align}
  & =\left( \dfrac{30}{4+2} \right)km/hr \\
 & =\dfrac{30}{6}=5km/hr \\
\end{align}$

Note: You can do this question quickly by assuming Abhay speed be x and framing equation according to the question in one variable as,
Let Abhay’s speed be x km/hour.
Then, according to question,
\[\begin{align}
  & \Rightarrow \dfrac{30}{x}-\dfrac{30}{2x}=\left( 2+1 \right)hours \\
 & \Rightarrow \dfrac{30}{x}-\dfrac{30}{2x}=3 \\
 & \Rightarrow \dfrac{60-30}{2x}=3 \\
 & \Rightarrow \dfrac{30}{2x}=3 \\
 & \Rightarrow 30=6x \\
 & \therefore x=5km/hour \\
\end{align}\]