📄 03 - SET-1 Race & Circular Motion, p.1

🎯 Problem 1:

In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s respectively. After how much time will they meet next?

(A) 140 sec
(B) 20 sec
(C) 40 sec
(D) 70 sec

✅ Relative Speed – Key Concept

• Relative Speed applies only to problems where two objects are moving towards or away from each other.
• In relative speed problems, when two objects move in the same direction, it's called a chasing scenario. When they move in opposite directions, it's called a meeting scenario.

✅ Relative Speed (Like a Magnet)

• 2 objects moving in the same direction → Subtract the 2 Speeds.
• 2 objects moving in the opposite direction → Add the 2 Speeds.
• Remember: (S)ame → (S)ubtract

🎯 Problem 2:

Varun and Sandeep started for a car race from the same point, in the same direction, and at the same time on a circular track of length 1635 m with the speeds of 90 km/h and 108 km/h, respectively. After how much time (in seconds) will they meet again for the first time?

(A) 324
(B) 325
(C) 327
(D) 326

🎯 Problem 3:

In a circular race of 750 m, X and Y start from the same point and at the same time with speeds of 9 km/h and 13.5 km/h, respectively. If they are running in the same direction, then when will they meet again for the first time on the track?

(A) 750 sec
(B) 900 sec
(C) 500 sec
(D) 600 sec

🎯 Problem 4:

Atul gives Vishu a head-start of 20 seconds in a 900 m race and beats him by 135 m. While running the same race again, Atul gives a start of 189 m and beats him by 8 seconds. In how much time can Vishu complete the full race of 900 m?

(A) 3 minutes 10 seconds
(B) 2 minutes 50 seconds
(C) 3 minutes 20 seconds
(D) 3 minutes 19 seconds

• For linear race type problems, solve them using the equation method.
• The arrow marks in the equations represent the word "covers".
• The winner takes less time to finish the race than the loser.
• Since Vishu’s speed is constant in both cases, we can subtract the two equations.

🎯 Problem 5:

M and N walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. M and N walk at a speed of 5 rounds per hour and 2 rounds per hour, respectively. How many times will they cross each other before 6:30 a.m?

(A) 10
(B) 3
(C) 5
(D) 7

!300

🎯 Problem 6:

P and Q start running in opposite directions on a circular track from the same point. If their speeds are 10 m/s and 8 m/s respectively, then after what time will they meet if the length of the track is 1620 m?

(A) 110 sec
(B) 70 sec
(C) 120 sec
(D) 90 sec

🎯 Problem 7:

Arvind and Chetan started running simultaneously from the same point in the same direction on a circular track of length 210 m. If Arvind takes 180 seconds to complete one round, and Chetan takes 420 seconds to complete one round, after how much time will they meet for the first time at the starting point on the track?

(A) 10 mins
(B) 15 mins
(C) 21 mins
(D) 28 mins

• LCM of lap times → To find the first meeting time at the starting point, when both runners have completed whole laps and therefore meet simultaneously. It is because LCM is the smallest time that is a multiple of both individual lap times.
• Relative speed → To find the first meeting time anywhere on the track, not necessarily at the starting point.

🎯 Problem 8:

In a circular race of 4800 m, A and B start from the same point and at the same time with speeds of 36 km/h and 54 km/h. When will they meet again for the first time on the track if they are running in the opposite direction?

(A) 200 sec
(B) 205 sec
(C) 178 sec
(D) 192 sec

🎯 Problem 9:

Seema walks around a circular field at the rate of 3 rounds per hour, while Priya runs around it at the rate of 8 rounds per hour. They start in the same direction from the same point at 11:54 p.m. They shall first cross each other at:

(A) 12:06 p.m
(B) 12:00 a.m
(C) 12:06 a.m
(D) 11:59 p.m

Relative Speed Method:

🎯 Problem 10:

Two athletes are participating in a race on a circular track of 220 m. Ravi runs at the speed of 22 m/s, while Kapil runs at the speed of 11 m/s. They start from the same point, at the same time, and in the same direction. After how many seconds will they meet for the first time?

(A) 15 sec
(B) 16 sec
(C) 20 sec
(D) 24 sec

🎯 Problem 11:

In a circular race of 1600 m in length, Bhaskar and Vinay start with speeds of 27 km/h and 45 km/h starting at the same time from the same point. When will they meet for the first time on the track when running in the opposite directions and the same direction, respectively?

==(A) 1 min 20 sec, 5 min 40 sec ==
(B) 1 min 40 sec, 5 min 20 sec
(C) 2 min 40 sec, 5 min 40 sec
(D) 1 min 20 sec, 5 min 20 sec

🎯 Problem 12:

On a 2200 m long circular track, Sarita and Kavita drove their cycles from the same point but in opposite directions with the speeds 20 km/hr and 16 km/hr, respectively. After how much time will they meet again for the first time?

(A) 2 min 20 sec
(B) 3 min 20 sec
(C) 2 min 50 sec
(D) 3 min 40 sec

🎯 Problem 13:

P and Q take part in 400 m race. P runs at 12 km/hr. P gives Q a start of 20 m and still beats him by 13 seconds. The speed of Q is: (Round up to two decimal places.)

(A) 11.38 km/hr
(B) 10.29 km/hr
(C) 11.61 km/hr
(D) 10.87 km/hr

• For linear race type problems, solve them using the equation method.
• The arrow marks in the equations represent the word "covers".
• The winner takes less time to finish the race than the loser.