Dalbir Singh, a policeman, is 114 m behind a thief. Dalbir runs 21 m per minute while the thief runs 15 m per minute. In how many minutes will Dalbir catch the thief?

Introduction / Context:
This is a simple linear pursuit problem. The closing speed equals the difference of their speeds when both move in the same direction. Time to catch equals the gap divided by closing speed.

Given Data / Assumptions:

• Initial gap = 114 m.
• Policeman speed = 21 m/min; thief speed = 15 m/min.

Concept / Approach:
Relative speed (closing) = 21 − 15 = 6 m/min. Time = gap / relative speed in minutes.

Step-by-Step Solution:

Verification / Alternative check:
Distance each covers in 19 minutes: policeman 399 m, thief 285 m; difference equals 114 m—the initial gap—so they meet at that time.

Why Other Options Are Wrong:
16, 18, 21, 23 minutes do not match the exact ratio 114 : 6.

Common Pitfalls:
Adding speeds instead of taking the difference; using seconds instead of minutes inadvertently.

Final Answer:
19 min