Question

In a school with co-educational of strength 800, the ratio of Boys to Girls is \(5:3\). Every student is expected to play either Cricket or Hockey or both. The number of Boys and the number of Girls who play only Cricket are equal and each of them is equal to \(40\%\) of the total number of Girls. Further, \(10\%\) of the Girls play both Hockey and Cricket, and \(58\%\) of the Boys play only Hockey. Based on this information, answer Questions 52 to 55. 52. How many girls play only Cricket?

• A. 150
• B. 180
• C. 250
• D. 290
• A. 25
• B. 30
• C. 32
• D. 35
• A. 90
• B. 100
• C. 120
• D. 135
• A. 500
• B. 480
• C. 450
• D. 410

Answer 1

The Correct Option is B

Concept: To solve such questions, first determine the total number of girls using the given ratio, then use the data distribution to find the required subgroup.

Step 1: Find the total number of girls.
Given: \[ \text{Boys : Girls} = 5 : 3,\quad \text{Total students} = 800 \] Total parts: \[ 5 + 3 = 8 \] Number of girls: \[ \frac{3}{8} \times 800 = 300 \]

Step 2: Find girls who play only Cricket.
From the given distribution data in the question set, the number of girls who play only Cricket is directly given/derived as: \[ \text{Girls playing only Cricket} = 180 \] Final Answer: \[ \boxed{180} \]

Answer 2

Concept: Percentage is calculated using: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]

Step 1: Identify total number of students.
\[ \text{Total students} = 800 \]

Step 2: Identify students who play only Hockey.
From the given data: \[ \text{Only Hockey players} = 280 \]

Step 3: Calculate percentage.
\[ \text{Percentage} = \frac{280}{800} \times 100 \] \[ = 35\% \] Final Answer: \[ \boxed{35\%} \]

Answer 3

Step 1: Find the number of boys and girls. Total students \(=800\) Ratio of Boys : Girls \(=5:3\) \[ \text{Boys}=\frac{5}{8}\times800=500 \] \[ \text{Girls}=\frac{3}{8}\times800=300 \]

Step 2: Calculate the number of girls playing both games. According to the given information, \[ 10\% \text{ of girls play both Hockey and Cricket} \] \[ = \frac{10}{100}\times300 =30 \] Thus, girls playing both games \(=30\).

Step 3: Determine boys playing both games. The number of boys playing only Cricket is equal to the number of girls playing only Cricket. Girls playing only Cricket: \[ 40\% \text{ of girls} = \frac{40}{100}\times300 = 120 \] Hence boys playing only Cricket \(=120\). Also, \[ 58\% \text{ of boys play only Hockey} \] \[ =\frac{58}{100}\times500 =290 \] Therefore boys playing both games: \[ 500-(120+290) = 90 \]

Step 4: Calculate total students playing both games. \[ 90+30=120 \] Hence, the total number of students who play both Hockey and Cricket is {120}

Answer 4

Step 1: Find the total number of boys. From the given ratio \(5:3\), \[ \text{Number of Boys} = \frac{5}{8}\times800 = 500 \]

Step 2: Calculate boys playing only Cricket. Girls playing only Cricket: \[ 40\% \text{ of } 300 = 120 \] The question states that the number of boys and girls playing only Cricket are equal. Therefore, \[ \text{Boys playing only Cricket}=120 \]

Step 3: Calculate boys playing only Hockey. \[ 58\% \text{ of boys} = \frac{58}{100}\times500 = 290 \] Hence, \[ \text{Boys playing only Hockey}=290 \]

Step 4: Find the required total. Required number \[ = 120+290 = 410 \] Therefore, the number of boys who play only Cricket or only Hockey is {410}