Linear/Circular Race

Total Questions: 67

41. In a 140 m race, Pankaj runs at a speed of 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: [SSC CHSL 10/08/2023 (4th Shift)]

Correct Answer: (c) 2 m/s
Solution:

42. A, B and C run simultaneously, starting from a point, around a circular track of length 1200 m, at respective speeds of 2m/s, 4m/s and 6m/s. A and B run in the same direction, while C runs in the opposite direction to the other two. After how much time will they meet for the first time? [SSC CGL 17/07/2023 (2nd shift)]

Correct Answer: (a) 10 minutes
Solution:

43. Racer A and racer B run a race of 18 km on a circular track of length 800 m. Both complete one round in 200 sec and 250 sec, respectively. After how much time from the start will the faster person meet the slower person for the last time?  [SSC CGL 17/07/2023 (4th shift)]

Correct Answer: (b) 4000 sec
Solution:

Total round to complete the race = 1800/800 = 22.5 rounds
L.C.M (200 sec., 250 sec.) = 1000 sec.
In 1000 sec. Racer A completed 5 rounds.
In 1000 sec. Racer B completed 4 rounds.
L.C.M. (5, 4) = 20
Time when faster person meet slower person last time = 1000/5 × 20 = 4000 sec.

44. In a 1170 m race, Raman reaches the final point in 65 seconds and Mohan reaches the final point in 90 seconds. By how much distance does Raman beat Mohan? [SSC CGL 19/07/2023 (1st shift)]

Correct Answer: (a) 325m
Solution:

Total distance of race = 1170 m
Raman reaches the final points in 65 seconds.
Mohan reaches the final points in 90 seconds.
Mohan' speed = 1170/90 = 13m/s
Distance covered by Mohan in 65 seconds = 13 × 65 = 845m.
Raman beats Mohan by
= 1170 - 845 = 325m

45. Two persons started running on a circular track simultaneously with speeds of 20 m/s and 30 m/s in opposite directions. If the circumference of the circular track is 100 m, then find at how many distinct points they will cross each other ? [SSC CGL 19/07/2023 (2nd shift)]

Correct Answer: (d) 5
Solution:

46. Ashok runs 2⅔ times as fast as Bharat. If Ashok gives Bharat a head start of 160m, then how far must the winning post be so that Ashok and Bharat can reach it at the same time? [SSC CGL 19/07/2023 (4th shift)]

Correct Answer: (b) 256m
Solution:

47. P gives Q a head-start of 2 seconds in a 400 m race, but both finish the race at the same time. Find the time taken by P to finish the race if the speed of Q is 2 m/sec. [SSC CGL 20/07/2023 (3rd shift)]

Correct Answer: (a) 198 seconds
Solution:

Speed of Q is 2 m/sec
Then, in 2 second he runs 4 meter
So, total distance covered by Q
= 400 - 2 × 2 = 396 meter
Now, according to the questions,
Time taken by Q =  time taken by P
therefore, Time taken by P to complete
the race = 396/2 = 198 second

48. In a 200-m linear race, if A gives B a start of 25 m, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. How long does A take to run 200m? [SSC CGL 24/07/2023 (3rd shift)]

Correct Answer: (d) 77.5 seconds
Solution:

49. Having started from the same point and at the same time, two runners P and Q are running around a circular track of length 500 m in opposite directions with the speeds of 6 m/s and 10 m/s, respectively. If they exchange their speeds after meeting for the first time, who will reach the starting point first? [SSC CGL 25/07/2023 (4th shift)]

Correct Answer: (c) Both P and Q will reach at the same time
Solution:

50. In an 800 m race, the ratio of the speeds of two contestants Alka and Mira is 4 : 7. If Alka has a start of 520 m, then, Alka will win by: [Matriculation Level 30/06/2023 (Shift - 4)]

Correct Answer: (c) 310 m
Solution: