In a kilometer race P runs at 10 m/sec, Q runs at 5 m/sec then which…

The correct answer is Option (2) → (A) and (C) only

The race is 1 km = 1000 m. The time taken by each runner is distance ÷ speed:

    \( \displaystyle \text{P: } \frac{1000}{10} = 100 \text{ sec} \)

    \( \displaystyle \text{Q: } \frac{1000}{5} = 200 \text{ sec} \)

P finishes first. In those 100 sec, Q runs only

    \(5 \times 100 = 500\) m

so Q is \(1000 - 500 = 500\) m behind when P finishes.

So P wins the race in 100 sec and beats Q by 500 m.

Checking the statements

(A) P wins the race in 100 sec — Correct. P finishes first, in \(\frac{1000}{10} = 100\) sec.

(B) Q wins the race in 100 sec — Incorrect. Q takes 200 sec and finishes second.

(C) P defeats Q by 500 m — Correct. Q has run only 500 m when P finishes.

(D) Q defeats P by 500 m — Incorrect. P, not Q, wins the race.