Question

1. In a certain cricket tournament 45 matches were played. Each team played once against each of the other teams. The number of teams participated in the tournament is
(A) 8
(B) 10
(C) 12
(D) 210


2.If the radius of a circle is increased by 50%, the perimeter of the circle will increased by
(A) 20%
(B) 30%
(C) 40%
(D) 50%

Kindly show steps in detail.

Answer 1

1.
If n is number of teams participated
number of matches = sum of first n - 1 natural numbers
45 = n (n - 1 ) / 2
n² - n - 90 = 0
n² - 10n + 9n - 90 = 0
n( n - 10 ) + 9( n - 10 ) = 0
( n - 10 ) ( n + 9 ) = 0
number of teams = 10

2.
r is increased by 50%
new radius = 1.5r
new perimeter = 2π(1.5r) = 3πr
percentage increase in perimeter = ( ( 3πr - 2πr ) / 2πr ) 100
= 50%