Question

X takes 4 hours to reach destination A from destination B. Y takes 8 hours to reach destination A from destination B. What would be the ratio of speed of X:Y ?

• A. 2:1
• B. 1:2
• C. 1:3
• D. 3:1

Hint:

When distance is constant, the ratio of speeds is the inverse of the ratio of times taken. If \( T_X : T_Y = a : b \), then \( S_X : S_Y = b : a \). In this case, \( T_X : T_Y = 4:8 = 1:2 \), so \( S_X : S_Y = 2:1 \).

Answer 1

The Correct Option is A

Step 1: Understanding the Problem
We are given the time taken by two individuals, X and Y, to cover the same distance. We need to find the ratio of their speeds.

Step 2: Key Formula or Approach
The relationship between speed (S), distance (D), and time (T) is \( S = \frac{D}{T} \).
When the distance is constant, speed is inversely proportional to time. \[ S \propto \frac{1}{T} \] Therefore, the ratio of speeds is the inverse of the ratio of their times. \[ \frac{S_X}{S_Y} = \frac{T_Y}{T_X} \]
Step 3: Detailed Explanation
Let the distance between destination A and destination B be D.
Time taken by X (\(T_X\)) = 4 hours.
Time taken by Y (\(T_Y\)) = 8 hours.
Speed of X (\(S_X\)) = \( \frac{D}{T_X} = \frac{D}{4} \).
Speed of Y (\(S_Y\)) = \( \frac{D}{T_Y} = \frac{D}{8} \).
Now, let's find the ratio of their speeds, \( S_X : S_Y \). \[ \frac{S_X}{S_Y} = \frac{D/4}{D/8} \] \[ \frac{S_X}{S_Y} = \frac{D}{4} \times \frac{8}{D} \] \[ \frac{S_X}{S_Y} = \frac{8}{4} = \frac{2}{1} \] So, the ratio of the speed of X to the speed of Y is 2:1.
Using the inverse proportion method:
\[ \frac{S_X}{S_Y} = \frac{T_Y}{T_X} = \frac{8}{4} = \frac{2}{1} \] Ratio \( S_X : S_Y = 2:1 \).

Step 4: Final Answer
The ratio of the speed of X:Y is 2:1. Therefore, option (A) is the correct answer.