In a kilometer race P runs at 10 m/sec, Q runs at 5 m/sec then which of the following statement(s) is/ are correct ?
(A) P wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below:
In a kilometer race P runs at 10 m/sec, Q runs at 5 m/sec then which of the following statement(s) is/ are correct ?
(A) P wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below:
Solution
Given information:
- P's speed = 10 m/sec
- Q's speed = 5 m/sec
- Race distance = 1 km = 1000 m
Checking Statement (A): P wins the race in 100 sec
Time = Distance ÷ Speed
Time taken by P = 1000 ÷ 10 = 100 seconds
Statement (A) is correct.
Checking Statement (B): Q wins the race in 100 sec
Time taken by Q = 1000 ÷ 5 = 200 seconds
Q takes 200 seconds, not 100 seconds. Q is also slower than P.
Statement (B) is incorrect.
Checking Statement (C): P defeats Q by 500 m
When P finishes the race in 100 seconds, the distance covered by Q is:
Distance covered by Q = Speed × Time
Distance covered by Q = 5 × 100 = 500 m
The gap between them = 1000 - 500 = 500 m
Statement (C) is correct.
Checking Statement (D): Q defeats P by 500 m
Q is slower than P, so Q cannot defeat P.
Statement (D) is incorrect.
Statements (A) and (C) are correct.
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