Question

Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference downwards. Find when they will again come together in the same position.

Accepted Answer

B. Time taken for 1 revolution by each wheel: - First wheel: 60 rev/min = 1 rev/sec $\implies 1$ second. - Second wheel: 36 rev/min = $\frac{36}{60} = \frac{3}{5}$ rev/sec $\implies \frac{5}{3}$ seconds. - Third wheel: 24 rev/min = $\frac{24}{60} = \frac{2}{5}$ rev/sec $\implies \frac{5}{2}$ seconds. They will come together after $	ext{LCM}\left(1, \frac{5}{3}, \frac{5}{2}ight)$ seconds. $$	ext{LCM of fractions} = \frac{	ext{LCM of numerators}}{	ext{HCF of denominators}} = \frac{	ext{LCM}(1, 5, 5)}{	ext{HCF}(1, 3, 2)} = \frac{5}{1} = 5	ext{ seconds.}$$

Revolutions of three wheels

Explanation

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