A policeman chases a thief on a straight road. The policeman catches the thief in 15 minutes if he drives with a speed of 60 km/h and catches the thief in 0.5 hours if he drives with a speed 45 km/h. What should be his driving speed (in km/h) to catch the thief in just 10 minutes?

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 26 Jun, 2024 Shift 1)

Answer 1

Given:

Speed of policeman = 60 km/h, time = 15 minutes (0.25 hours)

Speed of policeman = 45 km/h, time = 0.5 hours

Time to catch the thief = 10 minutes (1/6 hours)

Let Speed of thief = x km/hr.

Speed of policemen as v km/hr when to catch in 10 minutes.

Formula used:

Relative Speed = Speed of Policeman - Speed of Thief

Distance = Relative Speed × Time

Calculation:

Relative speed = 60 - x and 45 -x in two cases respectively.

Set the distances equal for both cases:

0.25(60 - x) = 0.5(45 - x)

⇒ x = 30 km/h (thief's speed)

To catch the thief in 10 minutes:

7.5 = (v - 30) × 1/6

⇒ v = 75 km/h

∴ The required speed is 75 km/h.

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