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: Write the speeds as a ratio.
Rohan's speed : Mohan's speed \( = 7.5 : 8 = 15 : 16 \) after multiplying both parts by 2 to clear the decimal.

Step 2: Use the fact that they travel for the same time.
Since distance = speed times time, and both travel for the same amount of time from the same point, their distances at any instant stay in the same ratio as their speeds.
So Rohan's distance : Mohan's distance \( = 15 : 16 \) at every moment.

Step 3: Represent the distances using one unknown.
Let Rohan's distance be \( 15k \) and Mohan's distance be \( 16k \) for some number k.
The gap between them at that moment is \( 16k - 15k = k \).

Step 4: Use the given gap to find k.
We are told the gap is 20 m, so \( k = 20 \).

Step 5: Find Mohan's distance.
\[ 16k = 16 \times 20 = 320 \text{ m} \]

Final Answer:
Mohan has travelled 320 meters, the same result reached here using the ratio of speeds instead of first finding the time. \[ \boxed{320 \text{ m}} \]