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.
Players who play chess but not cricket is approximately what percent of total players?

Options

A. `35%`
B. `45%`
C. None of these
D. `40%`

Answer

To solve the problem step by step, we will analyze the information given in the passage and use it to find the required percentage of players who play chess but not cricket.

### Step-by-Step Solution:

1. **Identify Total Players in Tennis:**
- Total number of players who play tennis = 160.

2. **Calculate Players Who Play All Three Games:**
- Players who play all three games (tennis, cricket, chess) = 10% of total tennis players.
- Calculation: \( 10\% \times 160 = 16 \) players.

3. **Establish the Ratio of Cricket to Chess Players:**
- The ratio of cricket to chess players is given as 3:5.
- Let the number of cricket players be \( 3x \) and chess players be \( 5x \).

4. **Total of Cricket and Chess Players:**
- The total of cricket and chess players is 100% more than tennis players.
- Calculation: \( 3x + 5x = 160 + 160 = 320 \).
- Therefore, \( 8x = 320 \) which gives \( x = 40 \).
- Thus, the number of cricket players = \( 3x = 120 \) and chess players = \( 5x = 200 \).

5. **Calculate Players Who Play Both Tennis and Chess:**
- Players who play both tennis and chess = \( 12.5\% \) of total tennis players.
- Calculation: \( 12.5\% \times 160 = 20 \) players.

6. **Set Up the Ratio of Players Who Play Both Tennis & Cricket to Chess & Cricket:**
- Let players who play both tennis & cricket be \( 2y \) and players who play both chess & cricket be \( 3y \).

7. **Total of Players Who Play Both Tennis & Cricket and Chess & Cricket:**
- Total = \( 2y + 3y = 5y \).
- This total is equal to one-fourth of chess players.
- Calculation: \( 5y = \frac{1}{4} \times 200 = 50 \).
- Thus, \( y = 10 \).
- Therefore, players who play both tennis & cricket = \( 2y = 20 \) and players who play both chess & cricket = \( 3y = 30 \).

8. **Determine Players Who Play Only Chess:**
- Total chess players = 200.
- Players who play chess and cricket = 30.
- Players who play chess and tennis = 20.
- Players who play all three games = 16.
- Therefore, players who play chess but not cricket = Total chess players - (Players who play chess and cricket + Players who play chess and tennis - Players who play all three).
- Calculation: \( 200 - (30 + 20 - 16) = 200 - 34 = 166 \).

9. **Calculate the Percentage of Players Who Play Chess but Not Cricket:**
- Total players = Tennis + Cricket + Chess = \( 160 + 120 + 200 = 480 \).
- Percentage of players who play chess but not cricket = \( \frac{166}{480} \times 100 \).
- Calculation: \( \frac{166}{480} \approx 0.3458 \times 100 \approx 34.58\% \).

### Final Answer:
Approximately 35% of the total players play chess but not cricket.