CAT Questions on Races With Solutions:
Question 1: In a 200 m race, Abhay beats Chetan by 40m and Chetan beats Kundan by 20 m. If Abhay and Kundan were to run a 500 m race, then by what distance will Abhay beat Kundan?
Question 2: X, Y and Z ran a 50 m race. The time taken by X was recorded by watch W1 and the time taken by Y and Z was recorded by watch W2. The time taken by X, Y and Z to complete the race according to the respective watches used was 5, 6 and 3 seconds respectively. W2 is a faulty clock and loses time uniformly. If X beats Y by 10 m, what was the speed of Z during the race?
Question 3: Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m. After the start of the race, A meets B for the first time at the end of the third minute. If A and B start the race from the same point, find the time taken by A to finish the race.
a) 19 minutes
b) 9.5 minutes
c) 27 minutes
d) 13.5 minutes
Question 4: In 1 km race, in which A,B, C are running, A beats B by 100 m, B beats C by 100 m. In the next kilometer race, C starts at the starting line, B starts 100 m behind the starting line and A starts 100 m behind B. Find the distance (in m) by which the winner is ahead of the person just behind him.
Question 5: Ram can beat Shyam by 40 meters in a race. If Ram starts from a point which is 20 metres behind the start line and Shyam starts from the start line, Ram will still beat Shyam by 24 metres. What is the length of their race?
a) 100 m
b) 150 m
c) 200 m
d) 250 m
e) 500 m
Solutions for CAT Questions on Races With Solutions:
1) Answer (C)
In the time that Abhay runs 200 m, Chetan runs 160m so the ratio of speeds of Abhay and Chetan is 5:4
In the time Chetan runs 200m, Kundan runs 180m. So the ratio of speeds of Chetan and Kundan is 10:9
Thus we can say that in the time that Chetan runs 160m, Kundan runs 160*9/10 = 144 m
Thus in a 200 m race, Abhay will Kundan by 56m. Thus in a 500 m race, Abhay will beat Chandan by 56*2.5 = 140m
2) Answer (A)
Speed of X = 50/5 = 10 m/s
Speed of Y = 40/5 = 8 m/s
Time taken by Y to finish the race = 50/8 = 6.25 s
It is now known that the faulty clock lost time and has shown 6s instead of 6.25s for Y.
Similarly the time taken by Z = 3 * 6.25/6 = 3.125s
Speed of Z = 50/3.125 = 16 m/s.
3) Answer (D)
Let the speed of A be ‘2s’ m/s. Speed of B = ‘s’ m/s
Relative speed between A and B = 2s – s = s m/s
Time taken for A to meet B = length of the track / relative speed between A and B = 800 / s = 3 minutes
=> 800 / s = 180
=> s = 800/180 m/s
So, time taken by A to finish the race = 7200 / 2*(800/180) = 7200 * 180 / 2*800 = 9 * 90 seconds = 810 seconds = 13.5 minutes
4) Answer (A)
Let the time taken by A = t
Speed of A = 1000/t
Speed of B = 900/t
Speed of C = 900*9/10/t = 810/t
Time taken by C in the second race = 100t/81.
Time taken by B in the second race = 11t/9.
Time taken by A in the second race = 12t/10.
Out of these 12t/10 is the lowest. Hence A wins the race.
B is the second in race.
Distance covered by B in 12t/10 = 900/t*12t/10 = 1080
Distance = 1000+100-1080 = 20 m
5) Answer (C)
Let the length of the race be l
In the time that Ram travels l metres, Shyam travels l-40 metres.
In the time that Ram travels l+20 metres, Shyam travels l – 24 metres.
From these two equations we can see that in the time that Ram travels 20 metres, Shyam travels 16 metres.
So for every 20 metres travelled by Ram Shyam will be left behind by 4 metres.
The final gap between Ram and Shyam is 40 metres, hence there has to be 10 intervals of such 20 metres.
Hence the length of the race is 20*10 = 200 metres