d Three wheels making 60 revolutions in a minute start
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Word Problem 5 (Wheels and revolutions times)

Shapes and volumes 0

Problem 5: Three wheels making 60,36,24,revolutions in a minute start with a certain point in their circumferences downward. They will first come all together again in the same position after;

a. 5 seconds                        b. 6 seconds                     c. 30  seconds             d.15 seconds

— Shapes and volumes — math aptitude test –

Solution:

Three wheels making 60 revolutions in a minute start ……

All three wheels make respective revolutions in a time of one minute or 60 seconds.

Lets take wheel which completes 36 revolutions in a minute !

\Rightarrow 36 revolutions = 60 seconds

\Rightarrow 1 revolution = \frac{60}{36}=\frac{5}{3}seconds

Similarly 1 revolution time for the wheel with 60 revolutions in one minute is !

\Rightarrow 1 revolution = \frac{60}{60}=\frac{1}{1}seconds

and

1 revolution time for the wheel with 24 revolutions in one minute is !

\Rightarrow 1 revolution = \frac{60}{24}=\frac{5}{2}seconds

Now we arrange 1 revolution time for all three wheels as;

\frac{5}{3},  \frac{1}{1},  \frac{5}{2}

\Rightarrow \frac{10}{6}, \frac{6}{6} , \frac{15}{6}

Now we find that LCM of numerators i-e 10, 6 and 15 is 30 and LCM of denominators i-e 6,6, and 6 is 6

So using formula;

LCM = \frac{ LCM of Numerators}{LCM of Denomenators}

we get;

LCM = \frac{ 30}{6} =5

So, after 5 seconds all three wheels will come at the same position



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