Given:
Munaf and Surya are running along a circular track.
They meet at the same point in 31st time and 43rd time.
The ratio of the speed of the faster boy to that of the slower one = n : 1
Concept used:
The time at which they meet is the LCM of the difference between their meeting times.
As every time they meet they cover the same distance, we can use this concept.
Solution:
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.
Now, we check for each value 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 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.