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1. 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 $2 \frac{1}{2}$ km per hour, 3 km per hour and 2 km per hour respectively. Then on the starting point all three will meet again after ?

A. 30 hours

B. 6 hours

C. 10 hours

D. 15 hours

Solution:

\begin{aligned} Distance  =  5 km \\ Speed of A  =  2 \frac{1}{2} km/hr \\ Time taken by A \\ = \frac{5}{5} \times 2 = 5 hours \\ Speed of B  =  3 km/hr \\ Time taken by B \\ = \frac{5}{3} hours \\ Speed of C  =  2 km/hr \\ Time taken by C \\ = \frac{5}{2} hours \\ \frac{LCM of numerator}{HCF of denominator} \\ = 2, \frac{5}{3}, \frac{5}{2} \\ LCM  = \frac{10}{1} = 10 \end{aligned}

They will meet again after 10 hours

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