Question

X and Y take part in 100 meter race. X runs at the speed of 6 kmph. X gives Y a start of 4 meter and still beats him by 4 seconds. The speed of Y is...........

• A. 5.0 kmph
• B. 5.4 kmph
• C. 5.6 kmph
• D. 6.0 kmph

Hint:

Remember the conversion factors: To convert from \textbf{km/hr to m/s}, multiply by \(\frac{5}{18}\). To convert from \textbf{m/s to km/hr}, multiply by \(\frac{18}{5}\). This is a very common conversion needed in speed-distance-time problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Problem
This is a problem about races and relative speeds. Let's break down the given information:


Total race distance = 100 m.
Speed of X (\(S_X\)) = 6 kmph.
Y gets a "start of 4 meter". This means Y only needs to run \(100 - 4 = 96\) meters.
X "beats him by 4 seconds". This means Y takes 4 seconds longer than X to finish his respective distance.
We need to find the speed of Y (\(S_Y\)).

Step 2: Key Formula or Approach
\begin{enumerate}
Convert X's speed from kmph to m/s.
Calculate the time taken by X to run the full 100 m.
Calculate the time taken by Y to run his 96 m.
Calculate Y's speed in m/s.
Convert Y's speed from m/s to kmph. \end{enumerate}
Step 3: Detailed Explanation
1. Convert X's Speed:
To convert kmph to m/s, we multiply by \(\frac{5}{18}\).
\[ S_X = 6 \text{ kmph} = 6 \times \frac{5}{18} = \frac{30}{18} = \frac{5}{3} \text{ m/s} \] 2. Calculate Time taken by X (\(T_X\)):
\[ T_X = \frac{\text{Distance}}{\text{Speed}} = \frac{100 \text{ m}}{5/3 \text{ m/s}} = 100 \times \frac{3}{5} = 20 \times 3 = 60 \text{ seconds} \] 3. Calculate Time taken by Y (\(T_Y\)):
X beats Y by 4 seconds, so Y takes 4 seconds more than X.
\[ T_Y = T_X + 4 = 60 + 4 = 64 \text{ seconds} \] 4. Calculate Y's Speed in m/s (\(S_Y\)):
Y runs 96 meters in 64 seconds.
\[ S_Y = \frac{\text{Distance run by Y}}{T_Y} = \frac{96 \text{ m}}{64 \text{ s}} = \frac{3 \times 32}{2 \times 32} = \frac{3}{2} = 1.5 \text{ m/s} \] 5. Convert Y's Speed to kmph:
To convert m/s to kmph, we multiply by \(\frac{18}{5}\).
\[ S_Y = 1.5 \text{ m/s} = \frac{3}{2} \times \frac{18}{5} = \frac{54}{10} = 5.4 \text{ kmph} \]
Step 4: Final Answer
The speed of Y is 5.4 kmph. Therefore, option (B) is the correct answer.