A survey of 500 TV viewers produced the following information.
285 viewers watch football games, 195 viewers watch hockey games, 115 viewers watch basketball game, 45 viewers watch football and basketball games, 70 viewers watch football and hockey games, 50 viewers watch hockey and basketball games, and 50 viewers do not watch any of three games. How many viewers watch exactly one of the three games?

Given: A survey of 500 TV viewers produced the following information. 285 viewers watch football games, 195 viewers watch hockey games, 115 viewers watch basketball game, 45 viewers watch football and basketball games, 70 viewers watch football and hockey games, 50 viewers watch hockey and basketball games, and 50 viewers do not watch any of three games.

Let number of viewers watch all three games = Z

Number of viewers in survey = 500

Number of Football viewers = 285
Number of Hockey viewers = 195
Number of Basketball viewers = 115
Number of viewers do not watch any games = 50
Number of viewers watch Football and Basketball games = 45
Number of viewers watch Football and Hockey games = 70
Number of viewers watch Hockey and Basketball games = 50

So,

Number of viewers watch only Football games = 285 - (45 - Z) - (70 - Z) - Z 

= 285 - 45 + Z - 70 + Z - Z

= 170 + Z

Number of viewers watch only Hockey games = 195 - (70 - Z) - (50 - Z) - Z 

= 195 - 70 + Z - 50 + Z - Z

= 75 + Z

Number of viewers watch only Basketball games = 115 - (45 - Z) - (50 - Z) - Z

= 115 - 45 + Z - 50 + Z - Z

= 20 + Z
Then,​​

500 = (45 -Z) + (50 -Z) + (70 - Z) +(170 + Z) +(75 + Z) + (20 + Z) + Z + 50

500 = 45 - Z + 50 - Z + 70 - Z +170 + Z + 75 + Z + 20 + Z + Z + 50 

500 = 480 + Z

Z = 20

Now,

Exactly one games = 170 + 20 + 75 + 20 + 20 + 20 = 325

325 viewers watch exactly one of the three games.

Thus, the correct answer is (d).

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