Question

In a group of 400 persons, 145 play Cricket, 200 play Football and 150 play Hockey. Each of them plays at least one of the three games and 15 persons play all the three games. What is the number of persons who play exactly two games?
a)80
b)65
c)70
d)90

Answer 1

so totaling up the number of people playing cricket, football, and hockey gives you 145+150+200=495 which is greater than 400. this is of course because some people play more than one sport.
we know that 15 people play all three, so we can subtract 15 from the total number of people, and the number of people in each sport (we already know everything there is to know about them so we might as well get rid of them!)

so now we have 385 total people, each who plays 1 or 2 sports. We also know that 130 play cricket, 135 play football, and 185 play hockey.
Totaling these new numbers gives us 495-45=450
so we have 385 people who can play 1 or 2 sports and 450 team spaces being filled

Now I'd say the easiest way to solve is with simple algebra
let x = number of people playing 1 sport
y = number of people playing 2 sports
x+y = 385
x + 2y = 450

just solve these equations for y to get your answer!

Answer 2

how did u get 385 ?

Answer 3

400 - 15. The total number of people is 400. Since 15 play in all 3 sports, we can neglect those 15 and therefore, the total possible number that can be in 2 sports is 385.

Answer 4

ohk thank u :)

Answer 5

exactly