Question

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

• A. 4.2
• B. 5.2
• C. 4.8
• D. 4.6

Answer 1

The Correct Option is C

To determine the distance Ravi will have run when Anil and Sunil meet again at the starting point, we need to calculate the time taken for Anil and Sunil to meet again. 

The circular path length is 3 km. Anil's speed is 15 km/hr, and Sunil's speed is 10 km/hr.

Step 1: Calculate the relative speed.
Since they are running in the same direction,
Relative speed = $|15 - 10| = 5$ km/hr.

Step 2: Time to meet again at the starting point is given by:
Time = $\frac{\text{Distance of track}}{\text{Relative Speed}} = \frac{3}{5} = 0.6$ hours.

Step 3: Calculate distance covered by Ravi in that time.
Ravi’s speed = 8 km/hr
Distance = Speed × Time = $8 \times 0.6 = 4.8$ km

Therefore, Ravi will have run 4.8 km when Anil and Sunil meet again at the starting point.

Answer 2

Given:

• Speed of Anil = 15 km/hr
• Speed of Sunil = 10 km/hr
• Speed of Ravi = 8 km/hr
• Length of the circular path = 3 km

Step 1: Find the ratio of speeds of Anil and Sunil
\[ \text{Anil : Sunil} = 15 : 10 = 3 : 2 \]

Step 2: When will they meet again?
Since the speed ratio is 3:2, they will meet again when Anil completes 3 rounds and Sunil completes 2 rounds.
So, distance run by Anil = \[ 3 \times 3 = 9\ \text{km} \]

Step 3: Time taken by Anil to cover 9 km
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{9}{15} = 0.6\ \text{hr} \]

Step 4: Distance covered by Ravi in 0.6 hr
Ravi’s speed = 8 km/hr
\[ \text{Distance} = \text{Speed} \times \text{Time} = 8 \times 0.6 = 4.8\ \text{km} \]

Final Answer: Ravi covers 4.8 km when Anil and Sunil meet again.

Correct Option: (C) 4.8