if certain number of boys are arranged evenly cyclical form, the 7th boy is directly opposite the 18th boy . How many boys are there?
Please i only need the solution
#thanks
If I give you only the solution, the whole point of this webpage would be futile. I assume you came here to learn and not just to receive answers. So please read this .....
Create a method by setting up a pattern starting with simple cases:
First of all , to have boys directly opposite each other, we must be able to form diagonals, thus we need an even number of boys
place 4 boys evenly spaced around a circle.
so 1 is opposite 3 , 2 is opposite 4
notice that 2(3-1) = 4
2(4-2) = 4
place 6 boys evenly spaced around a circle
so 1 is opposite 4, 2 is opposite 5, 3 is opposite 6
note 2(4-1) = 6
and 2(5-2) = 6
etc
so in our case, ......
tell me what you came up with.
The two boys are separated by 10 others on each side, right?
Now you can easily figure the solution.
thank alot Sir Reiny. Have gotten the right path with you explanation.
sir steve, i also appreciate.
Now i got 22 boys as the answer.
To find the number of boys, we need to use the concept of LCM (Least Common Multiple).
First, let's understand the given information. The 7th boy is directly opposite the 18th boy when arranged evenly in a cyclic form. This means that the distance between the 7th boy and the 18th boy is half the total number of boys.
Let's assume the number of boys is 'x'.
According to the given information, the distance between the 7th boy and the 18th boy is x/2.
Now, since the boys are arranged in a cyclic form, the distance between them is equal to the number of boys minus their distance, which is x - (x/2).
We know that the distance between them is equal to x - (x/2), so we can set up the following equation:
x - (x/2) = x/2
Simplifying the equation:
2x - x = x/2
x = x/2
To solve for 'x', we can multiply both sides of the equation by 2:
2x = x
x = 0
But this doesn't make sense since we can't have zero boys.
Let's try a different approach. Since the 7th boy is directly opposite the 18th boy, it means that the number of boys can be evenly divided into two groups. Group 1 consists of the 7 boys before the 7th boy and Group 2 consists of the 18 boys after the 18th boy.
So, we can set up the equation:
x = 7 + 18
Simplifying the equation:
x = 25
Therefore, there are 25 boys in total.