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In a college camp, 30 players play all three sports viz; cricket, football, and hockey. 140 players play exactly one sport and total players who play only football and only hockey are 75. If a total of 120 players play cricket, then how many players play cricket along with exactly one more sport?

In a college camp, 30 players play all three sports viz; cricket, football, and hockey. 140 players play exactly one sport and total players who play only football and only hockey are 75. If a total of 120 players play cricket, then how many players play cricket along with exactly one more sport? Correct Answer 25

GIVEN:

30 players play all three sports viz; cricket, football, and hockey.

140 players play exactly one sport and total players who play only football and only hockey are 75. 120 players play cricket.

CONCEPT:

Venn diagram

CALCULATION:

Players who play exactly one sport = a + b + c = 140

Players who play only football and only hockey = a + b = 75

⇒ Players who play only Cricket = 140 – 75 = 65

[ alt="F1 Maanik.G 30-07-2020 Savita D10" src="//storage.googleapis.com/tb-img/production/20/08/F1_Maanik.G_30-07-2020_Savita_D10.png" style="width: 191px; height: 216px;">

Total players who play cricket = 120

∴ Total players play cricket along with at least one more sport = 120 – 65 – 30

= 25

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