Question

600 players participated in four different events: volleyball, table tennis, badminton, and lawn tennis. The ratio between male and female players was 11:4 in volleyball, and 10% of the female players participated in table tennis. The remaining female players participated in badminton and lawn tennis in a ratio of 1:3. The ratio of male players who participated in volleyball and other events together is 3:5. 4% of those male players who did not participate in volleyball participated in lawn tennis. The remaining male players participated in table tennis and badminton in a ratio of 5:3. What is the total number of players participating in table tennis and volleyball together?

• A. 360
• B. 358
• C. 374
• D. 394
• E. 412

Hint:

When solving for total participants in multiple events, add the numbers from each group (male, female) in each event. Ensure to break down the groups carefully using the given ratios and percentages.

Answer 1

The Correct Option is D

Step 1: Given Data
- Total number of players = 600 - Ratio between male and female players is 11:4 in volleyball. - 10% of the female players participated in table tennis. - The remaining female players participated in badminton and lawn tennis in a ratio of 1:3. - The ratio of male players who participated in volleyball and other events together is 3:5. - 4% of those male players who did not participate in volleyball participated in lawn tennis. We are required to find the total number of players participating in table tennis and volleyball. Step 2: Calculate the number of male and female players.
From the given total number of players (600), we can calculate the number of male and female players: \[ \text{Total ratio} = 11 + 4 = 15 \] \[ \text{Number of male players} = \frac{11}{15} \times 600 = 440 \] \[ \text{Number of female players} = \frac{4}{15} \times 600 = 160 \] Step 3: Female players participating in table tennis.
10% of the female players participated in table tennis: \[ \text{Female players in table tennis} = 0.10 \times 160 = 16 \] Step 4: Male players participating in volleyball.
The number of male players who participated in volleyball is given as 165. From the first graph, we can verify this: \[ \text{Male players in volleyball} = 165 \] Step 5: Female players participating in volleyball.
The number of female players who participated in volleyball is given as 48. From the first graph, we can verify this: \[ \text{Female players in volleyball} = 48 \] Step 6: Total number of players in volleyball and table tennis.
The total number of players participating in volleyball and table tennis together is the sum of: - Male players in volleyball: 165 - Female players in volleyball: 48 - Male players in table tennis: 165 - Female players in table tennis: 16 Thus: \[ \text{Total in volleyball and table tennis} = 165 + 48 + 165 + 16 = 394 \] Step 7: Conclusion
Thus, the total number of players participating in volleyball and table tennis together is 394. Therefore, the correct answer is (D).