A thief is spotted by a policeman from a distance of 400 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief is 32 km/h and that of the policeman is 40 km/h, then how far would the thief have run before he is overtaken?  

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 1)
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  1. 1500 m
  2. 1000 m
  3. 1200 m
  4. 1600 m

Answer (Detailed Solution Below)

Option 4 : 1600 m
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Detailed Solution

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Given:

Distance between policeman and thief = 400 m

Speed of policeman =  40 km/h

Speed of thief = 32 km/h

Formula used:

Distance = relative speed × time

Calculation:

Distance = relative speed × time

⇒ 400 = (40 - 32) × (5/18) × time

⇒ 400 = 8 × (5/18) × time

⇒ Time = (400 × 18)/40 = 180 sec

Distance travelled by thief = 32 × (5/18) × 180

⇒ 32 × 5 × 10 = 1600 m 

∴ The correct answer is 1600 m.

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