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
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Correct Answer: Both P and Q will reach at the same time
Solution : Two runners P and Q run in a circular track of length with speeds 6 m/s and 10 m/s. The time they meet for the first time $=\frac{\text{Length of Circular Track}}{\text{Relative Speed}}$ $= \frac{500}{10 + 6} = \frac{500}{16} = \frac{125}{4}$ sec Now, Distance covered by P $= 6\times \frac{125}{4}=\frac{375}{2}$ m And distance covered by Q $=10\times \frac{125}{4}=\frac{625}{2}$ m After interchanging their speeds, Speed of P = 10 m/s Speed of Q = 6 m/s The remaining distance for P and Q will be equal to (500 – Distance covered respectively) Time taken by P to reach the starting point $= (500-\frac{375}{2})\times\frac{1}{10}$ $= \frac{625}{20}=\frac{125}{4}$ sec Time taken by Q to reach the starting point $=(500-\frac{625}{2})\times\frac{1}{6}$ $= \frac{375}{12} = \frac{125}{4}$ sec $\therefore$ They will reach the starting point at the same time. Hence, the correct answer is both P and Q will reach at the same time.
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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
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
Question : Ram and Shyam are racing along a circular track. The speed of Ram is thrice the speed of Shyam. The length of the circular track is 1440 m. After simultaneously starting the race from the same point, Ram meets Shyam for the first time at the end of the 8th minute. If Ram and Shyam start the race again from the same starting point simultaneously, then the time taken by Shyam to finish the race is: (given that the length of the race is the same as the length of the track)
Option 1: 7.5 minutes
Option 2: 16 minutes
Option 3: 30 minutes
Option 4: 22.5 minutes
Question : In a circular race of 4225 m, X and Y start from the same point and at the same time, at speeds of 54 km/hr and 63 km/hr, respectively. When will they meet again for the first time on the track, when they are running in opposite directions?
Option 1: 140 seconds
Option 2: 150 seconds
Option 3: 130 seconds
Option 4: 120 seconds
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
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