Question

Number of players who scored less than or equal to 40 runs in tournament Q is _____ % more than the number of players who scored more than 60 runs in tournament P and Q together.

• A. 65
• B. 50
• C. 40
• D. 45
• A. 7 : 15
• B. 5 : 14
• C. 4 : 15
• D. 3 : 5
• A. 210
• B. 270
• C. 240
• D. 235
• A. 140
• B. 130
• C. 120
• D. 105
• A. 180
• B. 160
• C. 190
• D. 210

Answer 1

The Correct Option is C

To solve the problem, we need to find out the difference in the number of players in two specific categories from tournaments P and Q, then calculate the percentage increase. 

1. First, understand the categories:
   • "Less than or equal to 40 runs in tournament Q": This will be the total players minus those who scored more than 40 runs in Q.
   • "More than 60 runs in tournaments P and Q together": We need the combined number of players scoring more than 60 in P and Q.
2. Given table details:
   • Number of players scoring more than 60 runs:
     1. In Tournament P: 25% of 300 = \(0.25 \times 300 = 75\)
     2. In Tournament Q: 25% of 300 = \(0.25 \times 300 = 75\)
   • Combining players scoring more than 60 in P and Q: \(75 + 75 = 150\)
3. Calculate players scoring less than or equal to 40 in Tournament Q:
   • Total players = 300
   • Players scoring more than 40 in Q = 30% of 300 = \(0.3 \times 300 = 90\)
   • Thus, players scoring 40 or less in Q = Total players - More than 40 = \(300 - 90 = 210\)
4. Determine the percentage increase:
   • Players scoring 40 or less in Q = 210
   • Players scoring more than 60 in P and Q = 150
   • The difference is \(210 - 150 = 60\)
   • Percentage increase: \(\left(\frac{60}{150}\right) \times 100 = 40\%\)
5. Therefore, the number of players who scored less than or equal to 40 runs in tournament Q is 40% more than the number of players who scored more than 60 runs in tournaments P and Q combined. Thus, the correct answer is 40.

Answer 2

To solve the problem of finding the ratio between the number of players who scored more than 60 runs in tournament Q and the number of players who scored less than or equal to 20 runs in tournaments Q and R combined, follow these steps: 

1. Identify the total number of players:
   • Total players in all tournaments is 300.
2. Calculate the number of players who scored more than 60 runs in tournament Q:
   • Percentage of players scoring more than 60 runs in Q = 25%.
   • Number of such players = \(300 \times \frac{25}{100} = 75\).
3. Calculate the number of players who scored less than or equal to 20 runs in tournaments Q and R:
   • In tournament Q:
     • Players scoring more than 20 runs = 60%.
     • Players scoring less than or equal to 20 runs = 100% - 60% = 40%.
     • Number of such players = \(300 \times \frac{40}{100} = 120\).
   • In tournament R:
     • Players scoring more than 20 runs = 70%.
     • Players scoring less than or equal to 20 runs = 100% - 70% = 30%.
     • Number of such players = \(300 \times \frac{30}{100} = 90\).
   • Total players scoring less than or equal to 20 runs in tournaments Q and R = 120 + 90 = 210.
4. Find the ratio of players:
   • Ratio = Number of players scoring >60 runs in Q : Number of players scoring ≤20 runs in Q and R.
   • Ratio = 75 : 210.
   • Simplify the ratio by finding the greatest common divisor:
     • The greatest common divisor of 75 and 210 is 15.
     • Simplified ratio = \(\frac{75}{15} : \frac{210}{15} = 5 : 14\).
5. Conclusion:
   • The correct answer is the ratio 5 : 14, which matches option 5 : 14.

Answer 3

To find the total number of players who scored more than 60 runs in all three tournaments (P, Q, and R), we will break down the problem step-by-step.

1. First, let's extract the data from the provided table regarding the percentage of players scoring more than 60 runs in each tournament:
   • Tournament P: 25%
   • Tournament Q: 25%
   • Tournament R: 20%
2. The total number of players is 300. We need to find how many of these scored more than 60 runs in all the three tournaments.
3. According to the problem, players who scored more than 60 runs in all three tournaments would be the intersection of the categories.
4. To calculate the number of players, multiply the percentage of players scoring more than 60 runs by the total number of players for each tournament:
   • In Tournament P, players scoring more than 60 runs = \left( \frac{25}{100} \right) \times 300 = 75
   • In Tournament Q, players scoring more than 60 runs = \left( \frac{25}{100} \right) \times 300 = 75
   • In Tournament R, players scoring more than 60 runs = \left( \frac{20}{100} \right) \times 300 = 60
5. To find the number of players who scored more than 60 runs in all three tournaments, we take the minimum of the above values since a player must be counted in all three tournaments to meet the criteria:
   • Minimum among 75, 75, and 60 is 60. Therefore, the number of players who scored more than 60 runs in each tournament is 60.
6. Thus, the total number of players who scored more than 60 runs in all three tournaments is 210.

Therefore, the correct answer is 210.

Answer 4

To solve this question, we need to determine the values of \( L \) and \( M \), where:

• \( L \) is the number of players who scored more than 40 runs in tournament P. 
• \( M \) is the number of players who scored less than or equal to 40 runs in tournament R.

Given that the total number of players is 300, let's analyze and calculate these values step-by-step:

Step 1: Calculate the Number of Players who Scored More than 40 Runs in Tournament P

• The table states that 35% of players scored more than 40 runs in tournament P.
• \(L = \frac{35}{100} \times 300 = 105\)

Step 2: Calculate the Number of Players who Scored Less than or Equal to 40 Runs in Tournament R

• The table indicates that 30% of players scored more than 40 runs in tournament R.
• Thus, the percentage of players who scored less than or equal to 40 runs is:
• \(100\% - 30\% = 70\%\)
• Therefore, \(M = \frac{70}{100} \times 300 = 210\)

Step 3: Calculate \( M - L \)

• Now, we simply subtract \( L \) from \( M \):
• \(M - L = 210 - 105 = 105\)

Therefore, the value of \( M - L \) is 105.

Conclusion

Based on the calculations above, the correct answer is 105.

Answer 5

To determine the average number of players who scored more than 20 runs in all three tournaments, we need to calculate the number of such players for each tournament and then find the average.

1. Understanding the data: Given, the percentage of players scoring more than 20 runs in each tournament:
   • Tournament P: 80%
   • Tournament Q: 60%
   • Tournament R: 70% 
2. Calculate the number of players scoring more than 20 runs:
   • Tournament P: \(300 \times \frac{80}{100} = 240\)
   • Tournament Q: \(300 \times \frac{60}{100} = 180\)
   • Tournament R: \(300 \times \frac{70}{100} = 210\)
3. Calculate the average: 
   The average number of players who scored more than 20 runs is calculated as: \(\frac{240 + 180 + 210}{3} = \frac{630}{3} = 210\)
4. Conclusion: The average number of players scoring more than 20 runs in all three tournaments is 210, which matches the correct answer given in the options.

Therefore, the correct answer is 210.