Question

When Mohan started chasing a thief, the thief was 200 metres ahead of Mohan. Mohan was running at the speed of 18 km/hr while thief was running at 9 km/hr. After 20 seconds, Mohan increased his speed to 27 km/hr. How much time did Mohan take in total to chase the thief?

• A. 50 seconds
• B. 30 seconds
• C. 45 seconds
• D. 55 seconds

Answer 1

The Correct Option is A

Time Taken by Mohan to Catch the Thief

Step 1: Understanding the Problem

- The initial distance between Mohan and the thief is 200 meters.
- Mohan’s initial speed is 18 km/hr, and the thief’s speed is 9 km/hr.

Step 2: Converting Speeds to m/s

- Mohan’s speed:

\[ 18 \text{ km/hr} = \frac{18 \times 1000}{3600} = 5 \text{ m/s} \]

- Thief’s speed:

\[ 9 \text{ km/hr} = \frac{9 \times 1000}{3600} = 2.5 \text{ m/s} \]

Step 3: Relative Speed Calculation

The relative speed between Mohan and the thief is:

\[ \text{Relative Speed} = 5 - 2.5 = 2.5 \text{ m/s} \]

Step 4: Time Taken to Cover the Initial Distance

To cover the initial 200 meters gap:

\[ \text{Time} = \frac{200}{2.5} = 80 \text{ seconds} \]

Step 5: Speed Increase After 20 Seconds

After 20 seconds, Mohan’s speed increases to 27 km/hr.

- Converting 27 km/hr to m/s:

\[ 27 \text{ km/hr} = \frac{27 \times 1000}{3600} = 7.5 \text{ m/s} \]

- The new relative speed is:

\[ 7.5 - 2.5 = 5 \text{ m/s} \]

Step 6: Calculating Distance Covered in First 20 Seconds

Distance covered in 20 seconds with the initial relative speed:

\[ 5 \text{ m/s} \times 20 = 100 \text{ meters} \]

- Remaining distance to cover is:

\[ 200 - 100 = 100 \text{ meters} \]

Step 7: Time Taken to Cover the Remaining Distance

Time required to cover the remaining 100 meters:

\[ \text{Time} = \frac{100}{5} = 20 \text{ seconds} \]

Step 8: Total Time Calculation

Total time taken = Time in the first phase + Time in the second phase

\[ 20 + 30 = 50 \text{ seconds} \]

Conclusion:

The total time taken by Mohan to catch the thief is 50 seconds.