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Three wheels can complete 60, 36, 24 revolutions per minute, respectively. There is a red spot on each wheel that touches the ground at time zero. After how much time all these spots will simultaneously touch the ground again?

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\frac{5}{2} \sec

\frac{5}{3} \sec

6 \sec

7.5 \sec

answer is C.

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Detailed Solution

Given,
Revolution per minute of first wheel = 60
Revolution per minute of second wheel = 36
Revolution per minute of third wheel = 24
Now, time needed to complete one resolution
First wheel

t_{1} = \frac{60}{60} = 1 \sec

(since 1 min= 60 second)
For, second wheel

t_{2} = \frac{36}{60} s = \frac{3}{5} \sec

For third wheel

t_{3} = \frac{24}{60} = \frac{2}{5} \sec

Now, the time at which the spot of all touch the ground at same time =

LCM of (\frac{1}{1}, \frac{3}{5}, \frac{2}{5})

= \frac{LCM of 1, 3, 2}{HCF  of 1, 5, 5}

= \frac{6}{1}

= 6 \sec

Hence, required time is 6 seconds.
Correct option is 3.

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