We are given that the time taken by Ravi and Sahil to complete a 100 m race is in the ratio of 5:7. Also, the faster runner took 50 seconds. Let's solve this step by step:

(i) Time taken by the slower runner:

The ratio of their times is 5:7. Let the time taken by the faster runner be $5x$ and the time taken by the slower runner be $7x$.

We know that the faster runner took 50 seconds, which means: $5x = 50 \quad \Rightarrow \quad x = \frac{50}{5} = 10$

Now, the time taken by the slower runner is: $7x = 7 \times 10 = 70 \text{ seconds}$

So, the slower runner took 70 seconds.

(ii) Speed of the faster runner:

The speed $v$ of a runner is calculated using the formula: $v = \frac{\text{Distance}}{\text{Time}}$ Here, the distance is 100 meters and the time taken by the faster runner is 50 seconds. Therefore, the speed of the faster runner is: $v = \frac{100}{50} = 2 \, \text{m/s}$

Thus, the speed of the faster runner is 2 meters per second.

Summary:

1. The time taken by the slower runner is 70 seconds.
2. The speed of the faster runner is 2 m/s.

Would you like more details or explanations?

Here are 5 related questions:

1. What is the speed of the slower runner?
2. If the race was 200 meters, how much time would the faster runner take to complete it?
3. What is the ratio of their speeds?
4. If Ravi increased his speed by 20%, how much faster would he complete the 100 m race?
5. How much distance did the faster runner cover after 30 seconds?

Tip: Always remember the basic formula for speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.