Munaf and Surya start simultaneously at the same point on a circular track and run along the track in the same direction. The point on the track at which they meet for the 31st time is the same as that at which they meet for the 43rd time. If the ratio of the speed of the faster boy to that of the slower one is n : 1, where ‘n’ is a natural number, which of the following is NOT a possible value of ‘n’?

Correct option is D

As they meet at the same point in 31st time and 43rd time we get the LCM of their meeting point as
LCM = 43 - 31 = 12.
For n = 5:
The difference between the speed of the faster boy to the slower one, if the speed of the faster boy is 5x and that of slower one is x ,is
= 5x - x 
= 4x.
As 4 is a factor of 12, n = 5 is a possible value.
For n = 3:
The difference between the speed of the faster boy to the slower one, if the speed of the faster boy is 3x and that of slower one is x is
= 3x - x 
= 2x.
As 2 is a factor of 12, n = 3 is a possible value.
For n = 6:
The difference between the speed of the faster boy to the slower one, if the speed of the faster boy is 6x and that of slower one is x is
= 6x - x 
= 5x.
As 5 is not a factor of 12, n = 5 is not a possible value.
For n = 4:
The difference between the speed of the faster boy to the slower one, if the speed of the faster boy is 4x and that of slower one is x is
= 4x - x 
= 3x.
As 3 is a factor of 12, n = 4 is a possible value.
∴ n = 6 is not a possible value of n.