Question:
After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time.
I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.
After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time.
I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.
I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.
Show Hint
Find out what each statement gives: Statement I describes both motions but not the track, while Statement II can supply the length of the track once the speed pattern is known.
Updated On: Nov 4, 2026
- The question can be answered with the help of one statement alone.
- The question can be answered with the help of any one statement independently.
- The question can be answered with the help of both statements together.
- The question cannot be answered even with the help of both statements together.
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Gati's distance second by second:
Gati's speed in seconds 1, 2, 3, ... is 2, 2.5, 3, 3.5, ... m/s (speed rises by 0.5 m/s at the end of each second).
Distance after t seconds: 2, 4.5, 7.5, 11, 15, 19.5, 24.5, 30, 36, 42.5, 49.5, 57, 65 for t = 1, 2, ..., 13.
Tez covers 5t: 5, 10, 15, ..., 65.
Step 2: Is Statement I enough?:
The gap (Tez - Gati) is 3, 5.5, 7.5, 9, 10, 10.5, 10.5, 10, 9, 7.5, 5.5, 3, 0 at t = 1, ..., 13. They meet when this gap is 0 or a whole number of track lengths. The length of the track is not given, so if the track is shorter than 10.5 m Tez would lap Gati earlier. Statement I alone cannot give the meeting time.
Step 3: Is Statement II enough?:
Statement II alone says nothing about Tez, and it only gives the lap length if Gati's speed pattern (Statement I) is known. So II alone is not enough.
Step 4: Use both:
Gati completes a lap in 10 s, so the track length = Gati's distance in 10 s = 42.5 m. The maximum gap before t = 13 is 10.5 m, which is less than 42.5 m, so Tez never laps Gati before the gap closes. The gap becomes 0 at t = 13 s, so they meet after 13 seconds.
Step 5: Conclusion:
Both statements are needed together, and together they are sufficient.
Final Answer:
The correct option is (3): The question can be answered with the help of both statements together.
Gati's speed in seconds 1, 2, 3, ... is 2, 2.5, 3, 3.5, ... m/s (speed rises by 0.5 m/s at the end of each second).
Distance after t seconds: 2, 4.5, 7.5, 11, 15, 19.5, 24.5, 30, 36, 42.5, 49.5, 57, 65 for t = 1, 2, ..., 13.
Tez covers 5t: 5, 10, 15, ..., 65.
Step 2: Is Statement I enough?:
The gap (Tez - Gati) is 3, 5.5, 7.5, 9, 10, 10.5, 10.5, 10, 9, 7.5, 5.5, 3, 0 at t = 1, ..., 13. They meet when this gap is 0 or a whole number of track lengths. The length of the track is not given, so if the track is shorter than 10.5 m Tez would lap Gati earlier. Statement I alone cannot give the meeting time.
Step 3: Is Statement II enough?:
Statement II alone says nothing about Tez, and it only gives the lap length if Gati's speed pattern (Statement I) is known. So II alone is not enough.
Step 4: Use both:
Gati completes a lap in 10 s, so the track length = Gati's distance in 10 s = 42.5 m. The maximum gap before t = 13 is 10.5 m, which is less than 42.5 m, so Tez never laps Gati before the gap closes. The gap becomes 0 at t = 13 s, so they meet after 13 seconds.
Step 5: Conclusion:
Both statements are needed together, and together they are sufficient.
Final Answer:
The correct option is (3): The question can be answered with the help of both statements together.
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