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A can run 1 km in 4 min 54 sec and B in 5 min. How many metres start can A can give B in a km race so that the race may end in a dead heat ?

  1. 16 m

  2. 18 m

  3. 20 m

  4. 22 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance covered by B in 6 sec $= \dfrac{(1000}{300}×6)=20 m$

AI explanation

A's time for 1 km is 4 min 54 sec = 294 seconds; B's time is 5 min = 300 seconds. For a dead heat, both must reach the finish line at the same time (300 seconds, B's full time). In 300 seconds, A (running at 1000/294 m/s) covers 300 x 1000/294 ≈ 1020.4 m — that is, A would finish 1000 m and cover roughly 20.4 more meters before B's 300 seconds are up. So A can give B a head start of about 20 m and still have both finish together. The other options (16, 18, 22 m) come from slightly miscalculating the extra distance A covers in the additional 6 seconds; 20 m is the value that correctly balances the two runners' speeds over the race duration.

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