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 female players participating in volleyball and badminton?

• A. 68
• B. 67
• C. 58
• D. 72
• E. 88

Hint:

When calculating the number of participants in different categories, always break down the percentages and ratios carefully. Use the remaining percentage for dividing into smaller categories.

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 female players participating in volleyball and badminton. 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: Remaining female players.
The remaining female players participated in badminton and lawn tennis in a ratio of 1:3. So, the remaining 90% of female players is: \[ \text{Remaining female players} = 160 - 16 = 144 \] These 144 female players are divided in a 1:3 ratio for badminton and lawn tennis. Thus, we calculate: \[ \text{Female players in badminton} = \frac{1}{4} \times 144 = 36 \] \[ \text{Female players in lawn tennis} = \frac{3}{4} \times 144 = 108 \] Step 5: Female players in volleyball and badminton.
The total number of female players participating in volleyball and badminton is: \[ \text{Total female players in volleyball and badminton} = 48 + 36 = 72 \] Step 6: Conclusion.
Thus, the total number of female players participating in volleyball and badminton is \( 72 \), corresponding to option (D).