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45% players played in 1st world cup out of which 25 players played in only 1st world cup. 57.5% players played in 2nd world cup out of which 45 players played in only 2nd world cup. 72.5% players played in 3rd world cup out of which 110 players played in only 3rd world cup. Find the players who played in both 1st world cup and 2nd world cup but not in 3rd world cup, if total number of players is 400.

45% players played in 1st world cup out of which 25 players played in only 1st world cup. 57.5% players played in 2nd world cup out of which 45 players played in only 2nd world cup. 72.5% players played in 3rd world cup out of which 110 players played in only 3rd world cup. Find the players who played in both 1st world cup and 2nd world cup but not in 3rd world cup, if total number of players is 400. Correct Answer 40

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From the figure:

x + y + w + 25 = 0.45 × 400 = 180

x + z + w + 45 = 0.575 × 400 = 230

y + z + w + 110 = 0.725 × 400 = 290

And

x + y + z + w + 25 + 45 + 110 = 400

⇒ x + y + z + w = 220

Solving all 4 equations:

⇒ x = 40, y = 35, z = 65 & w = 80

Number of players who played in both 1st WC and 2nd WC but not in 3rd WC = x = 40

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