There are n stations in a carcular path. Two consecutive stations are connected by blue line and two non-consecutive stations are connected by red line. If no. of red lines is equal to 99 times number of blue line then value of nis
(1) 201 (2) 200 (3) 199 (4) 202
Answers
There are n stations in a carcular path. Two consecutive stations are connected by blue line and two non-consecutive stations are connected by red line.
To find : if the no of red lines is equal to 99 times no of blue line then the value of n is ...
solution : let number of blue lines = n
number of red lines = combination of two lines out n - number of blue lines
= ⁿC₂ - n
= n!/2!(n - 2)! - n
= n(n - 1)/2 - n
= (n² - n - 2n)/2
= n(n - 3)/2
a/c to question,
number of red lines = 99 × number of blue lines
⇒n(n - 3)/2 = 99n
⇒(n - 3)/2 = 99
⇒n = 201
Therefore the value of n is 201
Answer:
Here is your Answer....Hope it helps :))
Step-by-step explanation:
let number of blue lines = n
number of red lines = combination of two lines out n - number of blue lines
= ⁿC₂ - n
= n!/2!(n - 2)! - n
= n(n - 1)/2 - n
= (n² - n - 2n)/2
= n(n - 3)/2
a/c to question,
red lines = 99 × total blue lines
⇒n(n - 3)/2 = 99n
⇒(n - 3)/2 = 99
⇒n = 201