Question : In a 140 m race, Pankaj runs at a speed of $\frac{5}{2}$ m/s. He gives a start of 20 m to Arun and still defeats him by 4 seconds. The speed of Arun is:
Option 1: 1.75 m/s
Option 2: 1.25 m/s
Option 3: 2 m/s
Option 4: 1.5 m/s
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Correct Answer: 2 m/s
Solution :
Given, Speed of Pankaj = $\frac52$ m/s
Pankaj gives 20 m start to Arun.
Time taken by Pankaj = Time taken by Arun – 4 seconds
Time taken by Pankaj to cover 140 m = $\frac{140}{\frac52}$ = 56 sec
⇒ Time taken by Arun = 56 + 4 = 60 sec
Pankaj gives a start of 20 m to Arun
⇒ Distance covered by Arun = (140 – 20) = 120 m
⇒ Speed = $\frac{\text{Distance}}{\text{Time}}$ = $\frac{120}{60}$ = 2 m/s
Hence, the correct answer is 2 m/s.
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