From a point on a circular track 5km long A,B and C started running in the same direction at the same time with speed of 2¹/₂ km per hour, 3km per hour and 2km per hour respectively. Then on the starting point all three will meet again after ?

Explanation:-

$$\eqalign{ & {\text{Distance = 5 km}} \cr & {\text{Speed of A = 2}}\frac{1}{2}{\text{ km/hr}} \cr & {\text{Time taken by A}} \cr & {\text{ = }}\frac{5}{2} \times 2 = 5{\text{hours}} \cr & {\text{Speed of B = 3 km/hr}} \cr & {\text{Time taken by B}} \cr & {\text{ = }}\frac{5}{3}{\text{hours}} \cr & {\text{Speed of C = 2 km/hr}} \cr & {\text{Time taken by C}} \cr & {\text{ = }}\frac{5}{2}{\text{hours}} \cr & \frac{{{\text{LCM of numerator}}}}{{{\text{HCF of denominator}}}} \cr & = 2,\,\frac{5}{3},\,\frac{5}{2} \cr & {\text{LCM = }}\frac{{10}}{1} = 10 \cr}$$ They will meet again after 10 hours