Q1: Let r be the radius of the circular tracks. Length and breadth of the rectangular track are 4r and 2r respectively. Length (perimeter) of the rectangular track = 12r Length of the two circular tracks (figure of eight) = 4r If A and B have to reach their starting points at the same time,
(12r/a)=4*pi*r/b
(where a and b are the speeds of A and B respectively)
(b/a)=4pi/12
(b-a)*100/a
= 4.7% Hence, option 4.
Q2:
Let there be g girls and b boys.
Number of games between two girls = gC2
Number of games between two boys = bC2
∴ g(g – 1)/2 = 45
∴ g2 – g – 90 = 0
∴ (g – 10)(g + 9) = 0
∴ g = 10
Also, b(b – 1)/2 = 190
∴ b2 – b – 380 = 0
∴ (b + 19)(b – 20) = 0
∴ b = 20
∴ Total number of games = (g + b)C2 = 30C2 = 435
∴ Number of games in which one player is a boy and the other is a girl = 435 – 45 – 190 = 200 Hence, option 1.