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Study the given passage carefully & answer the questions in a sport Academy XY', there are some student who can play three games i.e tennis, cricket & chess. Total number of players who play tennis is 160 & all three games are played by 10% of total tennis players. Ratio of cricket to chess players is 3:5 and total of cricket & chess players is 100% more than tennis players. Players who play both tennis and chess are `12(1)/(2)%` of total tennis players. Ratio of players who play both tennis & cricket to players who play both chess & cricket is 2:3 & total of players who play both tennis & cricket and players who play both chess & cricket is equal to one-fourth of chess players.
What is the average no. of players who play only one game?

A

`139(2)/(3)`

B

`129(1)/(3)`

C

135

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will break down the information provided and calculate the average number of players who play only one game. ### Step 1: Determine the number of players for each game - Total players who play tennis = 160 - Players who play all three games (Tennis, Cricket, Chess) = 10% of Tennis players = 10% of 160 = 16 players. ### Step 2: Calculate the total number of players for Cricket and Chess - The ratio of Cricket to Chess players is given as 3:5. - Let the number of Cricket players be 3x and Chess players be 5x. - The total number of Cricket and Chess players is 100% more than Tennis players: - Total Cricket + Chess = 160 + 160 = 320. So, we have: \[ 3x + 5x = 320 \] \[ 8x = 320 \] \[ x = 40 \] Now, we can find the number of players: - Number of Cricket players = 3x = 3(40) = 120 - Number of Chess players = 5x = 5(40) = 200 ### Step 3: Determine the players who play both Tennis and Chess - Players who play both Tennis and Chess = 12.5% of total Tennis players = 12.5% of 160 = 20 players. ### Step 4: Determine the players who play both Tennis and Cricket and both Chess and Cricket - Let the number of players who play both Tennis and Cricket be 2y and those who play both Chess and Cricket be 3y (from the ratio 2:3). - The total of players who play both Tennis & Cricket and Chess & Cricket is equal to one-fourth of Chess players: - Total = 1/4 of Chess players = 1/4 of 200 = 50. So, we have: \[ 2y + 3y = 50 \] \[ 5y = 50 \] \[ y = 10 \] Now we can find the number of players: - Players who play both Tennis and Cricket = 2y = 2(10) = 20 - Players who play both Chess and Cricket = 3y = 3(10) = 30 ### Step 5: Calculate the number of players who play only one game - Players who play only Tennis = Total Tennis - (Players who play both Tennis & Cricket + Players who play both Tennis & Chess + Players who play all three) - = 160 - (20 + 20 + 16) = 160 - 56 = 104 - Players who play only Cricket = Total Cricket - (Players who play both Tennis & Cricket + Players who play both Chess & Cricket + Players who play all three) - = 120 - (20 + 30 + 16) = 120 - 66 = 54 - Players who play only Chess = Total Chess - (Players who play both Chess & Cricket + Players who play both Tennis & Chess + Players who play all three) - = 200 - (30 + 20 + 16) = 200 - 66 = 134 ### Step 6: Calculate the average number of players who play only one game - Total players who play only one game = Players who play only Tennis + Players who play only Cricket + Players who play only Chess - = 104 + 54 + 134 = 292 - Average number of players who play only one game = Total players who play only one game / 3 - = 292 / 3 = 97.33 ### Final Answer The average number of players who play only one game is approximately **97.33**. ---
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