Three rings complete 60, 36 and 24 revolutions in a minute. They start from a certain point in their circumference down wards. By what time they come together again in the same position?
Solution
✅ Correct Option: 1
Instead of revolutions per minute, find the time taken for one full revolution. There are 60 seconds in a minute. | Ring | Revolutions per minute | Time for one revolution | |---|---|---| | First | 60 | $\dfrac{60}{60}=1$ second | | Second | 36 | $\dfrac{60}{36}=\dfrac{5}{3}$ seconds | | Third | 24 | $\dfrac{60}{24}=\dfrac{5}{2}$ seconds | All three are back at the starting point together after the LCM of these three times. Using the formula for the LCM of fractions, $\text{LCM}=\dfrac{\text{LCM of numerators}}{\text{HCF of denominators}}=\dfrac{\text{LCM}(1,5,5)}{\text{HCF}(1,3,2)}=\dfrac{5}{1}=5$ Check: in 5 seconds the rings finish $5$, $3$ and $2$ complete revolutions, all whole numbers. $\text{Time}=5$ seconds