A persons P starts his journey from A and another person Q starts his journey from B, towards each other. The speeds of P and Q are 16 km/h and 25 km/h respectivley What is the ratio of time taken by P and Q to reach B and A respectively?

Options

A. `16:25`
B. `1:1`
C. `25:16`
D. `4:5`

Answer

To solve the problem of finding the ratio of the time taken by person P to reach point B and person Q to reach point A, we can follow these steps:

### Step 1: Understand the relationship between speed, distance, and time
The relationship between speed (S), distance (D), and time (T) is given by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
From this, we can derive time as:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 2: Define the speeds of P and Q
Given:
- Speed of P (S_P) = 16 km/h
- Speed of Q (S_Q) = 25 km/h

### Step 3: Set the distances
Let the distance from A to B be D. Since both P and Q are traveling towards each other, the distances they cover to reach each other will be the same (D).

### Step 4: Calculate the time taken by P and Q
Using the formula for time:
- Time taken by P to reach B (T_P):
\[ T_P = \frac{D}{S_P} = \frac{D}{16} \]
- Time taken by Q to reach A (T_Q):
\[ T_Q = \frac{D}{S_Q} = \frac{D}{25} \]

### Step 5: Find the ratio of time taken by P and Q
To find the ratio of time taken by P to the time taken by Q:
\[ \text{Ratio} = \frac{T_P}{T_Q} = \frac{\frac{D}{16}}{\frac{D}{25}} \]
The D cancels out:
\[ \text{Ratio} = \frac{25}{16} \]

### Step 6: Finalize the ratio
Thus, the ratio of the time taken by P to reach B and Q to reach A is:
\[ \text{Ratio} = 25 : 16 \]

### Conclusion
The final answer is that the ratio of time taken by P to reach B and Q to reach A is **25:16**.

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