A, B & C start together running along a circular track of 500 m at 8 km/hr, 5 km/hr & 3 km/hr respectively. After how much time will all three meet again at the starting point for the first time?
Answers
Answer:
Step-by-step explanation:
Correct option is
D
12 hours
Time taken by A=
3
12
hours =4 hours.
Time taken by B=
7
12
hours
Time taken by C=
13
12
hours
∴A,B,C will meet again after an interval.
= L.C.M. of (
1
4
,
7
12
and
13
12
) hours
=
H.C.F. of (7,13)
L.C.M. of (4,12,12)
=
1
12
hours
=12 hrs
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All three will meet again at the starting point for the first time after 0.03125 hours or 1 minute and 52.5 second.
Let's denote the time taken by A, B, and C to meet at the starting point for the first time as T.
We know that the distance covered by each person in T hours will be the same as the circumference of the circular track, which is 500 meters.
For A, the distance covered in T hours is given by:
Distance covered by A = Speed of A x Time taken by A = 8 km/hr x T
Since the distance covered by A is equal to the circumference of the circular track,
we have:
8 km/hr x T = 500 meters
Solving for T, we get:
T = 500 meters / (8 km/hr) = 0.0625 hours
Similarly, for B and C, we have:
Distance covered by B = Speed of B x Time taken by B = 5 km/hr x T
Distance covered by C = Speed of C x Time taken by C = 3 km/hr x T
Since all three meet at the starting point at the same time, we have:
Distance covered by A = Distance covered by B = Distance covered by C
Substituting the expressions for the distances covered by A, B, and C, we get:
8 km/hr x T = 5 km/hr x T = 3 km/hr x T
Solving for T, we get:
T = 500 meters / (8 km/hr + 5 km/hr + 3 km/hr) = 500 meters / 16 km/hr
T = 0.03125 hours
Therefore, all three will meet again at the starting point for the first time after 0.03125 hours or 1 minute and 52.5 seconds.
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