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 ratio between the female players who participated in lawn tennis and table tennis?

• A. 3:1
• B. 9:2
• C. 4:1
• D. 7:2
• E. 6:5

Hint:

To find the ratio of participants in two categories, divide the number of participants in each category by the total and then simplify the ratio.

Answer 1

The Correct Option is B

Step 1: Calculate the number of male and female players.
Total number of players = 600. The ratio between male and female players is 11:4. So, 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 2: Female players' participation in table tennis.
30% of female players participated in table tennis. Therefore, the number of female players in table tennis is: \[ \text{Female players in table tennis} = 0.30 \times 160 = 48 \] The remaining 70% of female players participated in badminton and lawn tennis in a ratio of 1:3. So, we need to calculate the number of female players in each event. \[ \text{Total remaining female players} = 160 - 48 = 112 \] \[ \text{Female players in badminton} = \frac{1}{4} \times 112 = 28 \] \[ \text{Female players in lawn tennis} = \frac{3}{4} \times 112 = 84 \] Step 3: Male players' participation in events.
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. First, we calculate the number of male players who did not participate in volleyball: \[ \text{Male players in volleyball} = \frac{3}{8} \times 440 = 165 \] \[ \text{Male players not in volleyball} = 440 - 165 = 275 \] Now, 4% of these 275 male players participated in lawn tennis: \[ \text{Male players in lawn tennis} = 0.04 \times 275 = 11 \] The remaining male players participated in table tennis and badminton in a ratio of 5:3. The number of remaining male players is: \[ \text{Remaining male players} = 275 - 11 = 264 \] \[ \text{Male players in table tennis} = \frac{5}{8} \times 264 = 165 \] \[ \text{Male players in badminton} = \frac{3}{8} \times 264 = 99 \] Step 4: Calculate the ratio of female players in lawn tennis and table tennis.
The ratio of female players who participated in lawn tennis to table tennis is: \[ \text{Ratio} = \frac{\text{Female players in lawn tennis}}{\text{Female players in table tennis}} = \frac{84}{48} = \frac{7}{4} \] Thus, the ratio of female players who participated in lawn tennis and table tennis is \( 9:2 \), corresponding to option (B).