‘A’ starts his journey at 1:00 p.m. from a location P with a speed of 1 m/sec. ‘B’ starts his journey from the same location P and along the same direction at 1:10 p.m. with a speed of 2 m/sec. If ‘B’ meets ‘A’ at the location Q, then the distance PQ is || || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS

‘A’ starts his journey at 1:00 p.m. from a location P with a speed of 1 m/sec. ‘B’ starts his journey from the same location P and along the same direction at 1:10 p.m. with a speed of 2 m/sec. If ‘B’ meets ‘A’ at the location Q, then the distance PQ is:

(A) 1.5 km 

(B) 1.75 km 

(C) 1.2 km 

(D) 1.25 km





Solution:

Let's solve the problem step by step.


1. Determine the time distance between the starts of A and B:

  • A starts at 1:00 p.m.
  • B starts at 1:00 p.m.
  • The time difference is 10 minutes, which is 600 seconds (since 1 minute= 60 seconds)
2. Calculate the distance A travels before B starts:
  • A's speed= 1 m/sec
  • Time= 600 seconds
  • Distance traveled by A

= Speed × Time
= 1m/sec × 600 sec
= 600 meters.


3. Calculate the relative speed of B with respect to A:
  • A's speed= 1m/sec
  • B's speed= 2m/sec
  • Relative speed of B with respect to A

= 2m/sec-1m/sec
= 1m/sec


4. Determine the time taken by B to catch up with A:
  • Distance to be covered by B to catch up with A= 600 meters
  • Relative Speed= 1m/sec

Time taken= Distance/Relative Speed

= 600 meterss/1m/sec

= 600 seconds

5. Calculate the total distance PQ:

  • In 600 seconds, B travels

= 2m/sec × 600 seconds

= 1200 meters

= 1.2 km


Therefore, the distance PQ is: (C) 1.2 km.


Importance of this question:

  • Enhances logical reasoning skills.
  • Strengthens time-distance concept understanding.
  • Essential for solving real-world travel problems.
  • Improves speed and accuracy in competitive exams.
  • Previously asked in ADRE SLRC 2022 Paper III for the Grade-III Post.


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