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Basic Statements

  1. A gives a start of 10 m to B  When B has already run 10 m, then A starts running.

In a race of 100 m, A gives a start of 10 m to B. Despite this, A wins the race by 20 m. What is the ratio of the speed of A and B?
Time taken by A to cover 70 m = Time taken by B to cover 100 m
Since the distance is constant, the ratio of speed of A and B = 10:7
  1. A gives a start of 10 seconds to B  B has already run for 10 seconds, now A starts running.

 Where v m/s is the speed of B.
In a 100 m race, Tom runs at a speed of 1.66 m/s. If Tom gives a start of 4 m to Jerry and still beats him by 12 s, what is the speed of Jerry?
Time taken by Tom to cover 100 m = 60 s
Now, since Tom beats Jerry by 12 s, time taken by Jerry = 72 s
And the distance covered by Jerry = 96 m
So, speed = 96/72 = 1.33 m/s

Karan and Arjun run a 100-m race where Karan beats Arjun by 10 m. To do a favour to Arjun, Karan starts 10 m behind the starting line in a second 100 m race. They both run at their earlier speeds. Which of the following is true in connection with the second race?
  1. Karan and Arjun reach the finishing line simultaneously.
  2. Arjun beats Karan by 1 m.
  3. Arjun beats Karan by 11 m.
  4. Karan beats Arjun by 1 m.
Situation (I)
In whatever time Karan covers a distance of 100 m, Arjun covers 90 m in the same time.

Situation (II)
Karan is 10 m behind the starting point. Once again to cover 100 m from this new point Karan will take the same time as before. In the same time Arjun will cover only 90 m. This means that both of them now will be at the same point, which is 10 m away from the finish point. Since both of them are required to cover the same distance of 10 m and Karan has a higher speed, he will beat Arjun. There is no need for calculations as option (4) is the only such option.

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