Question : Two people A and B started running from the same point on a circular track of length 400 m in opposite directions with initial speeds of 10 m/s and 40 m/s, respectively. Whenever they meet, A's speed doubles and B's speed halves. After what time from the start will they meet for the third time?
Option 1: 30 sec
Option 2: 24 sec
Option 3: 26 sec
Option 4: 28 sec
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Correct Answer: 26 sec
Solution : Given: Total length of the track = 400 m Speed of A = 10 m/sec Speed of B = 40 m/sec They are running in the opposite direction ⇒ Relative speed = 10 + 40 = 50 m/sec We know, Speed = $\frac{\text{Distance}}{\text{Time}}$ Time when they meet first time = $\frac{400}{50}$ = 8 sec Now, the speed of A will get doubled and that of B will get half. ⇒ The new speed of A = 20 m/sec And, the new speed of B = 20 m/sec ⇒ Relative speed = 20 + 20 = 40 m/sec Time when they meet second time = $\frac{400}{40}$ = 10 sec Now, again the speed of A will get doubled and that of B will get half. ⇒ New speed of A = 40 m/sec And, New speed of B = 10 m/sec ⇒ Relative speed = 40 + 10 = 50 m/sec ⇒ Time when they meet third time = $\frac{400}{50}$ = 8 sec ⇒ At the third time, they will meet after 8 + 10 + 8 = 26 sec Hence, the correct answer is 26 sec.
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