Question

Seema, Meena and Reena start jogging around a circular stadium and complete one round in $54$sec, $42$sec and $63$sec respectively. After approximately how many minutes they will meet again at the starting point ?
A.$8.5$minutes
B.$10.3$minutes
C.$3.9$minutes
D.$6.3$minutes
E.None of these

Answer 1

Hint: Here we are given that Seema, Meena and Reena start jogging around a circular stadium and complete one round in 54sec,42sec and 63sec respectively. So to find the time when they meet take the LCM of all three values. Try it, you will definitely get the answer.

Complete step-by-step answer:
Here we are given that Seema, Meena and Reena start jogging around a circular stadium and complete one round in 54sec,42sec and 63sec respectively.
To find how many minutes they will meet again at the starting point we have to find LCM of all the three values.
So factors of $54=2\times 3\times 3\times 3$.
Also, factors of $42=2\times 3\times 7$.
Again, factors of $63=7\times 3\times 3$.
So required LCM we get is,
LCM$=3\times 3\times 3\times 2\times 7=378$seconds
So let us convert seconds into minutes.
To convert seconds into minutes divide seconds value by $60$.
So $\dfrac{378}{60}=6.3$ minutes.
Seema, Meena and Reena start jogging around a circular stadium and complete one round in $54$sec, $42$sec and $63$sec respectively. After approximately $6.3$ minutes they will meet again at the starting point.
Therefore, the correct answer is option (D).

Additional information:
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers. LCM denotes the least common factor or multiple of any two or more given integers. LCM is used in the case when the denominators of the fractions are different. While performing any arithmetic operations such as addition, subtraction with fractions, LCM is used to make the denominators as the same numbers. This process makes the simplification process easier.


Note: The concept of LCM must be cleared. A common multiple is a number which is a multiple of two or more numbers. LCM denotes the least common factor or multiple of any two or more given integers. Also, to convert seconds into minutes divide seconds value by $60$.