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 =

\[\frac{\text{Total distance}}{\text{Distance covered in 1 day}} = \frac{360}{48} = 7 . 5 = \frac{75}{10} = \frac{15}{2} \text{days}\]

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

\[\frac{360}{60} = 6 \text{days}\]

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

Now, LCM of \[\left( \frac{15}{2}, 6\ \text{and}\ 5 \right) = \frac{\text{LCM of numerators}}{\text{HCF} \hspace{0.167em} \text{of denominators}} = \frac{30}{1} = 30 \text{days}\]

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