A, B, C, D, and E practice running at a stadium that has several tracks. Each one starts running from the same point Z. A runs around a path which is an equilateral triangle ZYX. B runs around a square path ZYWV. C runs on a regular pentagonal path ZYUTS. D runs on a regular hexagonal path ZYRQPO. E runs along the trapezium ZYPO and completes one round in 20 seconds. Among all the tracks, there is a common side ZY, having length 100 m. The ratio of speeds of B and C is 5 : 4 respectively whereas the ratio of the time taken by A and D to complete one round of their tracks is 3 : 4 respectively. E's speed is the same as B's speed whereas A's speed is half that of C's.Note: The athletes maintain the same speeds in any track.Q 113. If A, B and C start running in the same direction along a 300 m long circular track, then after how much time will they meet for the first time?a) 60 secondsb) 90 secondsc) 75 secondsd) 120 seconds
Question
A, B, C, D, and E practice running at a stadium that has several tracks. Each one starts running from the same point Z. A runs around a path which is an equilateral triangle ZYX. B runs around a square path ZYWV. C runs on a regular pentagonal path ZYUTS. D runs on a regular hexagonal path ZYRQPO. E runs along the trapezium ZYPO and completes one round in 20 seconds. Among all the tracks, there is a common side ZY, having length 100 m. The ratio of speeds of B and C is 5 : 4 respectively whereas the ratio of the time taken by A and D to complete one round of their tracks is 3 : 4 respectively. E's speed is the same as B's speed whereas A's speed is half that of C's.Note: The athletes maintain the same speeds in any track.Q 113. If A, B and C start running in the same direction along a 300 m long circular track, then after how much time will they meet for the first time?a) 60 secondsb) 90 secondsc) 75 secondsd) 120 seconds
Solution
To solve this problem, we first need to find the speed of each runner.
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We know that the speed of B is the same as E, and E completes a round in 20 seconds. Since the length of the side ZY is 100m, and the trapezium ZYPO has two sides of this length, the total length of the trapezium is 300m. Therefore, the speed of B (and E) is 300m/20s = 15m/s.
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The speed of C is 4/5 of B's speed, so C's speed is 4/5 * 15m/s = 12m/s.
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The speed of A is half of C's speed, so A's speed is 1/2 * 12m/s = 6m/s.
Now, we need to find out when A, B, and C will meet for the first time on a 300m long circular track. This will happen when they all complete a whole number of laps at the same time.
The time it takes for each runner to complete a lap is the length of the track divided by their speed:
- A: 300m / 6m/s = 50 seconds
- B: 300m / 15m/s = 20 seconds
- C: 300m / 12m/s = 25 seconds
The least common multiple of 50, 20, and 25 is 100. Therefore, A, B, and C will meet for the first time after 100 seconds. However, this option is not given in the question. There might be a mistake in the question or in the calculation.
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