Comprehension
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr
Question: 1
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.
At what time did X catch the thief?
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.
At what time did X catch the thief?
At what time did X catch the thief?
Show Hint
When X starts, the thief already has a head start of 15 minutes at 60 km/hr. X closes this gap at the difference of their speeds.
Updated On: Nov 4, 2026
- 3.30 p.m.
- 3.15 p.m.
- 3 p.m.
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Head start of the thief:
X starts at 12:15 p.m. In the first 15 min the thief covers \( 60 \times \dfrac{15}{60} = 15 \) km.
Step 2: Relative speed:
X closes the gap at \( 65 - 60 = 5 \) km/hr.
Step 3: Time to catch up:
\( \dfrac{15}{5} = 3 \) hr after X starts, which is 12:15 p.m. + 3 hr = 3:15 p.m.
Step 4: Check:
The thief runs from 12 noon to 3:15 p.m. (3.25 hr) at 60 km/hr, covering 195 km. X runs 3 hr at 65 km/hr, covering 195 km. They meet.
Final Answer:
The correct option is (2): 3.15 p.m.
X starts at 12:15 p.m. In the first 15 min the thief covers \( 60 \times \dfrac{15}{60} = 15 \) km.
Step 2: Relative speed:
X closes the gap at \( 65 - 60 = 5 \) km/hr.
Step 3: Time to catch up:
\( \dfrac{15}{5} = 3 \) hr after X starts, which is 12:15 p.m. + 3 hr = 3:15 p.m.
Step 4: Check:
The thief runs from 12 noon to 3:15 p.m. (3.25 hr) at 60 km/hr, covering 195 km. X runs 3 hr at 65 km/hr, covering 195 km. They meet.
Final Answer:
The correct option is (2): 3.15 p.m.
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Question: 2
If another policeman had started the same chase along with X, but at a speed of 60 km/hr, then how far behind was he when X caught the thief?
If another policeman had started the same chase along with X, but at a speed of 60 km/hr, then how far behind was he when X caught the thief?
Show Hint
The other policeman starts at the same time as X (12:15 p.m.) and rides until X catches the thief at 3:15 p.m. Compare the distances covered by the two.
Updated On: Nov 4, 2026
- 15 km
- 18.75 km
- 21 km
- 37.5 km
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: When and where X catches the thief:
X starts at 12:15 p.m. and catches the thief 3 hr later (head start 15 km, relative speed 5 km/hr), at 3:15 p.m. X has covered \( 65 \times 3 = 195 \) km.
Step 2: Distance covered by the other policeman:
He starts along with X at 60 km/hr, so in the same 3 hr he covers \( 60 \times 3 = 180 \) km.
Step 3: Gap:
\( 195 - 180 = 15 \) km. He is 15 km behind X (and the thief) at that moment.
Final Answer:
The correct option is (1): 15 km
X starts at 12:15 p.m. and catches the thief 3 hr later (head start 15 km, relative speed 5 km/hr), at 3:15 p.m. X has covered \( 65 \times 3 = 195 \) km.
Step 2: Distance covered by the other policeman:
He starts along with X at 60 km/hr, so in the same 3 hr he covers \( 60 \times 3 = 180 \) km.
Step 3: Gap:
\( 195 - 180 = 15 \) km. He is 15 km behind X (and the thief) at that moment.
Final Answer:
The correct option is (1): 15 km
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