ploease tell me by which method we can find the speed of the cycle.

Asked by ketagajjar | 5th Jul, 2010, 02:25: PM

Expert Answer:

Dear Student,
Let the number of days after which they will meet again at the starting point be T.
=> Distance travelled by 1st cyclist = 60T
distance travelled by 2nd cyclist = 72T
distance travelled by 3rd cyclist = 90T
Also, let the number of revolutions completed by three cyclists be x, y and z respectively.
Therefore,
Distance travelled by 1st cyclist = 360x
Distance travelled by 2nd cyclist = 360y
Distance travelled by 3rd cyclist = 360z
Now,
from above equations we have,
360x = 60T  => 6x = T ----(1)
and, 360y = 72T  => 5y = T -----(2)
and, 360z = 90T  => 4z = T -----(3)
from (1) and (2),
6x = 5y => x = 5y/6 ----(4)
from (2) and (3),
5y = 4z => y = 4z/5 ----(5)
Now, since x, y and z should all be integers,
from (4) we have,
y should be a multiple of 6 => y = 6k (where k is some integer)
similarly from (5), we have,
z should be a multiple of 5 => z = 5m (where m is some integer)
Now, the minimum value of m such that y = 4z/5 is a multiple of 6, is 3.
(when m = 3, z = 5x3 = 15 and y = 4x15/5 = 12 =  6x 2).
Hence, x = 5x12/6 = 10
therefore, x = 10, y = 12 and z = 15.
Now from (2) we have, T = 5y = 5x12 = 60 days.
Hence they will meet at starting point after 60 days.
Regards,
Topperlearning.

Answered by  | 15th Jul, 2010, 02:07: PM

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