A man walked at a speed of 4km/hr from point A to B and came back from point B to A at the speed of 6km/hr. What would be the ratio between the time taken by man in walking from point A to B to point B to A respectively ?

Options

A. `5:3`
B. `2:3`
C. `2:1`
D. `3:2`

Answer

To find the ratio between the time taken by the man in walking from point A to B and from point B to A, we can follow these steps:

### Step 1: Define the distance
Let the distance between point A and point B be \( d \) kilometers.

### Step 2: Calculate time taken from A to B
The speed from A to B is 4 km/hr. The time taken to travel from A to B can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Thus, the time taken from A to B is:
\[ T_{AB} = \frac{d}{4} \]

### Step 3: Calculate time taken from B to A
The speed from B to A is 6 km/hr. Similarly, the time taken to travel from B to A is:
\[ T_{BA} = \frac{d}{6} \]

### Step 4: Find the ratio of the times
To find the ratio of the time taken from A to B to the time taken from B to A, we can set up the ratio:
\[ \text{Ratio} = \frac{T_{AB}}{T_{BA}} = \frac{\frac{d}{4}}{\frac{d}{6}} \]

### Step 5: Simplify the ratio
When we simplify the ratio, the distance \( d \) cancels out:
\[ \text{Ratio} = \frac{d}{4} \times \frac{6}{d} = \frac{6}{4} = \frac{3}{2} \]

### Conclusion
The ratio of the time taken by the man in walking from point A to B to the time taken from point B to A is \( 3:2 \).

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