# A circular field has a circumference of 360 km.

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?

Solution:

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

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

Also, number of days taken by $3^{\text {rd }}$ cyclist to cover this distance $=\frac{360}{72}=5$ days

Now, $\operatorname{LCM}$ of $\left(\frac{15}{2}, 6\right.$ and 5$)=\frac{\operatorname{LCM} \text { of numerators }}{\mathrm{HCF} \text { of denominators }}=\frac{30}{1}=30$ days

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