Question

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?
A. $\dfrac{5}{2}$s
B. $\dfrac{5}{3}$s
C. 6 s
D. 7.5 s

Answer 1

Hint: In this equation use the given information and values and find the revolution completed by the wheel in one second Also remember to find the LCM of the revolutions completed by wheels in one seconds, use this information to approach towards the solution of the question.

Complete step-by-step answer:
According to the given information we know that three wheels are completing 60, 36, 24 revolutions per minute from the three wheels each have a red spot on them which touches ground at time 0
Let A, B and C be the three wheels completing revolution 60, 36 and 24 in a minute
Let’s find out the revolutions completed by the wheels in 1 second
For wheel A
Since it is completing the 60 revolution in 1 minute therefore
Revolution completed in 1 second = $\dfrac{{60}}{{60}}$= 1 revolution
For wheel B
Revolution completed by wheel B in 1 minute is equal to 36 therefore
Revolution completed by wheel B in 1 second =$\dfrac{{36}}{{60}}$ = $\dfrac{3}{5}$ revolution in one second
For wheel C
Revolution completed by wheel C in 1 minute is equal to 24 therefore
Revolution completed by wheel C in 1 second =$\dfrac{{24}}{{60}}$ = $\dfrac{2}{5}$ revolution in one second
So to find the time when red of each wheel will touch ground simultaneously let’s find the LCM of (1,$\dfrac{3}{5}$, $\dfrac{2}{5}$)
We know that LCM of fractional numbers are found as LCM of numerator/HCF of denominator
Therefore LCM of (1,$\dfrac{3}{5}$,$\dfrac{2}{5}$)
For numerator 1, 3, 2 let’s find the multiple of these numbers
Multiples of number 1 are 1, 2, 3, 4, 5, 6 multiple of 3 are 3, 6, 9, 12 and multiple of 2 are 2, 4, 6, 8, 10
Since the least common multiple in number 1, 3, 2 is 6 therefore LCM of numerator is 6
Now the HCF of denominator 1, 5, 5 let’s find the factors of these numbers
Factor of 1 are 1, factors of 5 are 1, 5
Since 1 is the common highest factor of number in 1, 5, 5 therefore HCF of denominator is 1
Therefore the LCM of (1,$\dfrac{3}{5}$,$\dfrac{2}{5}$) = 6
So after 6 sec red spot of each wheel will touch simultaneously
Hence option C is the correct option.

Note: In the above solution we used the terms “LCM and HCF” to find the solution these terms can be explained as, LCM stands Least Common Multiple as its name the common least multiple of the set of finite numbers is said to be the LCM of the set of finite numbers whereas the HCF stands for Highest Common Factor in this theory the common highest factor of the set of finite numbers is said to be HCF of the set of finite numbers.