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.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 6.
The time at which they meet is the L.C.M of the difference between their meeting points.
And, when they meet they cover the equal distance
Now,
As they meet at the same point in 31st time and 43rd time we get the L.C.M of their meeting point as
L.C.M = 43 - 31 = 12
Now, for the values of n
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 the slower boy is x
⇒ 5x - x = 4x
As 4 is the factor of 12, n = 5 is the 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 the slower boy is x
⇒ 3x - x = 2x
As 2 is the factor of 12, n = 3 is the 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 the slower boy is x
⇒ 4x - x = 3x
As 3 is the factor of 12, n = 4 is the 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 the slower boy is x
⇒ 6x - x = 5x
As 5 is the factor of 12, n = 6 is not the possible value
So, n = 6 is not the possible value of n