Question

A circular field of circumference 360 kilometres.Two cyclists abhay and ravi can going the speed of 12 kilometres per hour and 15 kilometres per hour respectively,round the field. After how many hours they will meet again at the starting point

Answer 1

Circumference of the circular field = 360 km
Speed of Abhay = 12 km/hr
Speed of Ravi = 15 km/hr
So time taken by Abhay to travel one round of circular field = $\frac{360}{12}=30\mathrm{hr}$
And time taken by Ravi to travel one round of circular field = $\frac{360}{15}=24\mathrm{hr}$
L.C.M. of 30 and 24 is given by;
$$\begin{gathered} 30=2\times 5\times 3 \\ 24=2\times 2\times 2\times 3 \end{gathered}$$
So L.C.M of 24 and 30 = $2\times 2\times 2\times 5\times 3=120$
Therefore after 120 hours both will meet at the starting point.