An inspector is 228 metres behind a thief. The inspector runs 42 metres per minute and the thief runs 30 metres per minute. After how many minutes will the inspector catch the thief?

Introduction / Context:
This is a classic chase or pursuit problem. It involves two people running in the same direction at different speeds, with one starting behind the other. The key idea is relative speed, which determines how quickly the distance between them closes. These problems are common in aptitude and reasoning tests.

Given Data / Assumptions:
The inspector is 228 metres behind the thief at the start.

Given Data / Assumptions:
The inspector runs at 42 metres per minute.
The thief runs at 30 metres per minute in the same direction.
Both maintain constant speeds and run on a straight path.
We are asked to find the time in minutes after which the inspector catches the thief.

Concept / Approach:
In a chase situation where both move in the same direction, the effective speed at which the gap closes is the difference between their speeds. This is called the relative speed. Once the relative speed is known, time to catch up can be found using time = distance divided by relative speed. Here, the initial distance is the head start of the thief over the inspector.

Step-by-Step Solution:
Step 1: Find the relative speed of the inspector with respect to the thief.Step 2: Relative speed = speed of inspector − speed of thief.Step 3: Relative speed = 42 − 30 = 12 metres per minute.Step 4: Initial distance between them is 228 metres.Step 5: Time taken to catch up = distance / relative speed.Step 6: Time = 228 / 12 minutes.Step 7: Compute 228 / 12 = 19 minutes.

Verification / Alternative check:
You can verify by computing how far each runs in 19 minutes. Inspector distance = 42 * 19 = 798 metres. Thief distance = 30 * 19 = 570 metres. The difference in the distances is 798 − 570 = 228 metres, which exactly equals the initial separation. This shows that after 19 minutes, the inspector has covered exactly 228 metres more than the thief and therefore catches him.

Why Other Options Are Wrong:
20 minutes would produce a distance difference of 12 * 20 = 240 metres, which overshoots the initial gap, so it does not match the exact moment of catching.
18 minutes would close only 12 * 18 = 216 metres, which leaves a remaining gap of 12 metres.
21 minutes gives 12 * 21 = 252 metres, again overshooting the required difference.
17 minutes closes just 12 * 17 = 204 metres, which is not enough for the inspector to catch the thief.

Common Pitfalls:
A typical mistake is to add the speeds instead of subtracting them, which would only be correct if they were running toward each other instead of in the same direction. Another error is mixing units, but here both speed and distance use metres and minutes consistently. Remember that for objects moving in the same direction, relative speed is the difference in their speeds.

Final Answer:
The inspector will catch the thief in 19 minutes.