Question

A survey of $500$ television viewers produced the following information, $285$ watch football, $195$ watch hockey, $115$ watch basket-ball, $45$ watch football and basket ball, $70$ watch football and hockey, $50$ watch hockey and basket ball, $50$ do not watch any of the three games. The number of viewers, who watch exactly one of the three games are

• A. 325
• B. 310
• C. 405
• D. 372

Answer 1

Answer: (A)

$a+e+f+g=285,b+d+f+g=195$
$c+d+e+g=115,e+g=45,f+g=70,d+g=50$
$a+b+c+d+e+f+g=500-50=450$
So $,a+f=240,b+d=125,c+e=65$
$a+e=215,b+f=145;b+c+d=165$
$a+c+e=255;a+b+f=335$
Solving we get
$b=95,c=40,a=190,d=30,e=25,f=50$
and $g=20$
Desired quantity $=a+b+c=325$