Question

A man covers a distance of 25 Km in an hour, partly on foot at the rate of 4 Km/hr and partly on a motorcycle at 32 km/hr. Find the distance travelled on the motorcycle.
(a) 14 km
(b) 32 km
(c) 24 km
(d) 9 km

Answer 1

Hint: Firstly, we should know the formula which we are going to use for the relation of time, speed and distance as $s=\dfrac{d}{t}$. Then, we can assume time ${{t}_{1}}$ be the time for which man is using a motorcycle and time ${{t}_{2}}$be the time for which the man is walking. Then, by using the formula for total time as $\dfrac{x}{32}+\dfrac{25-x}{4}=1$, we calculate the value of x which is assumed as the distance travelled by the motorcycle.

Complete step-by-step answer:
In this question, we are supposed to find the distance travelled by the man on a motorcycle in km.
Firstly, we know from the given data that man is travelling at the speed of 25 km/hr which means:
25 km = 1 hour
Now, we also know the speed of the walking and the speed of the motorcycle as:
Speed of walking= 4 km/hr
Speed of the motorcycle= 32 km/hr
Now, let us suppose that the distance travelled by the man by using the motorcycle in 1 hour be x km.
So, in 1 hour we already know that he travelled only 25 km total and if x km is travelled by motorcycle then the remaining will be travelled by walking only.
So, the distance covered by walking during the 1 hour= (25-x) km
Now, we know the relation between time(t), speed(s) and distance(d) as:
$s=\dfrac{d}{t}$
In this question, we know the total time taken to complete the journey is 1 hour.
So we take time ${{t}_{1}}$ be the time for which man is using a motorcycle and time ${{t}_{2}}$be the time for which the man is walking.
So, from the above fact the total time taken to cover a total distance of 25 km is 1 hour.
Then, we can conclude that the summation of time ${{t}_{1}}$ and ${{t}_{2}}$ gives us the total time as 1 hour:
${{t}_{1}}+{{t}_{2}}=1....\left( i \right)$
Now, we can find the value of the time ${{t}_{1}}$ by using the speed distance formula as speed by motorcycle is given as 32 km/hr:
$\begin{align}
  & 32=\dfrac{x}{{{t}_{1}}} \\
 & \Rightarrow {{t}_{1}}=\dfrac{x}{32} \\
\end{align}$
Similarly, we can find the value of the time ${{t}_{2}}$ by using the speed distance formula as speed by walking is given as 4 km/hr:
$\begin{align}
  & 4=\dfrac{25-x}{{{t}_{2}}} \\
 & \Rightarrow {{t}_{2}}=\dfrac{25-x}{4} \\
\end{align}$
Now, substitute the values of the time ${{t}_{1}}$ and ${{t}_{2}}$ in equation (i) as:
$\dfrac{x}{32}+\dfrac{25-x}{4}=1$
Now, the above equation gives the time for covering 25 km partly by foot an d partly by motorcycle.
Then, solve it for the value of x as:
$\begin{align}
  & \dfrac{x+8\left( 25-x \right)}{32}=1 \\
 & \Rightarrow x+200-8x=32 \\
 & \Rightarrow 168=7x \\
 & \Rightarrow x=24 \\
\end{align}$
So, the above calculation gives the value of the distance (x) travelled by the motorcycle is 24 km.
Hence, option (c) is correct.

Note: Here, the only condition that this question will go wrong is when we don’t know the relation between speed, distance and time. It is mandatory to learn some of the basic formulas to solve these kinds of questions as time and speed formulas. So, the basic relation between time, speed and distance is $s=\dfrac{d}{t}$ where s is speed, t is time and d is distance.