Question

if x ,y and a start at the same time in the same direction to run around a circular stadium x complete a round in 126 seconds, y in 154 second and z in 231 seconds all starting at the same point. after what time will they meet again at the starting point. how Many rounds would have x,y, and z completed by that time? ​

Answer 1

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Step-by-step explanation:

ANSWER

It is given that x completes a round in 126 seconds, y in 154 seconds and z in 231 seconds. Therefore,

126, 154 and 231 can be factorised as follows:

126=2×3×3×7

154=2×7×11

231=3×7×11

The time after which x,y and z meet is the LCM of the time taken by x,y and z to cover one round.

We know that LCM is the least common multiple, therefore, the LCM of 126, 154 and 231 is:

LCM=2×3×3×7×11=1386

Thus, time after which x,y and z will meet is 1386 seconds.

Now, the number of rounds covered can be obtained by dividing total time by time for each round, therefore,

Number of rounds of x is  

126

1386

​

=11

Number of rounds of y is  

154

1386

​

=9

Number of rounds of z is  

231

1386

​

=6