A thief is spotted by the police at a distance of 500m. On seeing the

1.	A thief is spotted by the police at a distance of 500m. On seeing the police, the thief takes off on a motor cycle at a speed of 30 m/s. If the thief is caught in 1 min 40 seconds, find the speed of the police.1. 43 km/hr2. 59 km/hr3. 78 km/hr4. 118 km/hr5. 126 km/hr
Answer» Correct Answer - Option 5 : 126 km/hr Given: Distance at which the thief is spotted = 500 m Speed of thief = 30 m/s Time taken by the police to catch the thief = 1 min 40 seconds = 100 s Concept used: Time taken for the police to catch the thief = distance/(relative speed) Relative speed = S_P– S_T, when both are going in same direction. Calculation: Time taken for the police to catch the thief = 500/(S_P – 30) = 100 s ⇒ 5 = S_P – 30 ⇒ S_P = 35 m/s ⇒ 35 m/s = 35 × (18/5) km/hr = 126 km/hr ∴ The required speed is 126 km/hr.

A thief is spotted by the police at a distance of 500m. On seeing the police, the thief takes off on a motor cycle at a speed of 30 m/s. If the thief is caught in 1 min 40 seconds, find the speed of the police.1. 43 km/hr2. 59 km/hr3. 78 km/hr4. 118 km/hr5. 126 km/hr

Answer» Correct Answer - Option 5 : 126 km/hr

Given:

Distance at which the thief is spotted = 500 m

Speed of thief = 30 m/s

Time taken by the police to catch the thief = 1 min 40 seconds = 100 s

Concept used:

Time taken for the police to catch the thief = distance/(relative speed)

Relative speed = S_P– S_T, when both are going in same direction.

Calculation:

Time taken for the police to catch the thief = 500/(S_P – 30) = 100 s

⇒ 5 = S_P – 30

⇒ S_P = 35 m/s

⇒ 35 m/s = 35 × (18/5) km/hr = 126 km/hr

∴ The required speed is 126 km/hr.

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