# Word Problem 5

**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: **

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 !

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

and

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

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

, ,

, ,

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;

we get;

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