Question

A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?

Answer 1

GIVEN: A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60, and 72 km a day, round the field.
TO FIND: When they meet again.

In order to calculate the time when they meet, we first find out the time taken by each cyclist in covering the distance.

Number of days 1^st cyclist took to cover 360 km = $\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Distance}\mathrm{covered}\mathrm{in}1\mathrm{day}}=\frac{360}{48}=7.5=\frac{75}{10}=\frac{15}{2}\mathrm{days}$

Similarly, number of days taken by 2^nd cyclist to cover same distance = $\frac{360}{60}=6\mathrm{days}$

Also, number of days taken by 3^rd cyclist to cover this distance = $\frac{360}{72}=5\mathrm{days}$
Now, LCM of $\left(\frac{15}{2},6\mathrm{and}5\right)=\frac{\mathrm{LCM}\mathrm{of}\mathrm{numerators}}{\mathrm{HCF}\hspace{0.17em}\mathrm{of}\mathrm{denominators}}=\frac{30}{1}=30\mathrm{days}$

Thus, all of them will take 30 days to meet again.