Question : A, B, and C run simultaneously, starting from a point, around a circular track of length 1200 m, at respective speeds of 2 m/s, 4 m/s, and 6 m/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?
Option 1: 10 minutes
Option 2: 9 minutes
Option 3: 12 minutes
Option 4: 11 minutes
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Correct Answer: 10 minutes
Solution : Circular Track length = 1200 m Speed of A = 2 m/s Speed of B = 4 m/s Speed of C = 6 m/s The relative speed of A and B = 4 – 2 = 6 m/s The relative speed of A and C = 2 + 6 = 8 m/s A and B will meet on the track after every = $\frac{1200}{2}$ = 600 s A and C will meet on the track after every = $\frac{1200}{8}$ = 150 s Thus, A, B, and C will meet together for the first time on the track after = LCM (600, 150) = 600 seconds $\therefore$ They will meet for the first time after = $\frac{600}{60}$ = 10 min Hence the correct answer is 10 minutes.
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Question : Having started from the same point simultaneously, two runners P and Q are running around a circular track of length 500 m in opposite directions with 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?
Option 1: Q
Option 2: P
Option 3: Both P and Q will reach at the same time
Option 4: No one of the P and Q
Question : Two friends, P and Q, start running around a circular track from the same point. They run in the same direction. P runs at 6 m/sec and Q runs at b m/sec. If they cross each other at exactly two points on the circular track and b is a natural number less than 6, how many values can b take?
Option 1: 2
Option 2: 1
Option 3: 4
Option 4: 3
Question : Sohan and Amit started a car race from the same point in the same direction and at the same time on a circular track of length 1125 m with speeds of 36 km/h and 54 km/h, respectively. After how much time (in seconds) will they meet for the first time since the start of the race?
Option 1: 220
Option 2: 215
Option 3: 210
Option 4: 225
Question : Two persons started running on a circular track at a speed of 20 m/s and 30m/s in opposite directions. If the circumference of the circular track is 100 m, find how many distinct points they will cross each other.
Option 2: 3
Option 3: 5
Option 4: 10
Question : Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 km/h and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
Option 1: 120 sec
Option 2: 110 sec
Option 3: 100 sec
Option 4: 90 sec
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