Question

Three persons A, B and C run along a circular path $ 12 $ km long. They start their race along the same point at the same time with a speed of $ 3 $ km/hr, $ 7 $ km/hr and $ 13 $ km/hr respectively. After what time will they meet again?
A. $ 16 $ hours
B. $ 24 $ hours
C. $ 9 $ hours
D. $ 12 $ hours

Answer 1

Hint: Here we are given three persons with three different speeds and we are asked to find when these three will meet so first we will find the total time taken by an individual and then will take the LCM (Least Common Multiple) of the numerator part and the HCF (Highest common Factor) for the denominator part and will take its ratio for the resultant required value.

Complete step by step solution:
Time taken can be expressed as the distance travelled open the speed.
Time taken by the person A $ = \dfrac{{12}}{3} = \dfrac{4}{1} $ hours … (A)
Similarly, time taken by the person B $ = \dfrac{{12}}{7} $ hours …. (B)
Similarly, time taken by the person C $ = \dfrac{{12}}{{13}} $ hours …. (C)
Given that A, B, C will meet again after an interval $ = \dfrac{{LCM\;{\text{of (4,12,12)}}}}{{HCF\;{\text{of (7,13)}}}} $
Know the difference between the HCF and LCM properly and apply accordingly. HCF is the greatest or the largest common factor between two or more given numbers whereas the LCM is the least or the smallest number with which the given numbers are exactly divisible.
Meeting Point $ = \dfrac{{12}}{1} $ hours
Hence from the given multiple choices, the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Don’t be confused between the LCM and HCF concepts, be good in multiples and division. Always remember while simplification of any fraction, common multiples from the numerator and the denominator cancels each other.