Question

Rohan travels 30 meters in 4 seconds, whereas Mohan travels 40 meters in 5 seconds. If both start from the same point, what distance would be travelled by Mohan by the time he is 20 meters ahead of Rohan?

• A. 320 m
• B. 300 m
• C. 280 m
• D. 250 m

Hint:

Work out each one's speed, then find how fast the gap between them grows, and use time = gap divided by that rate.

Answer 1

The Correct Option is A

Step 1: Find each person's speed.
Rohan's speed \( = \frac{30}{4} = 7.5 \) m/s.
Mohan's speed \( = \frac{40}{5} = 8 \) m/s.

Step 2: Find how fast the gap between them grows.
Both start from the same point and move the same way, so the gap between them grows at the rate of Mohan's speed minus Rohan's speed.
Gap growth rate \( = 8 - 7.5 = 0.5 \) m/s.

Step 3: Find the time needed for the gap to reach 20 m.
\[ t = \frac{20}{0.5} = 40 \text{ seconds} \]

Step 4: Find the distance Mohan covers in that time.
Distance = speed times time.
\[ 8 \times 40 = 320 \text{ m} \]

Final Answer:
Mohan travels 320 meters by the time he is 20 meters ahead of Rohan. \[ \boxed{320 \text{ m}} \]