Total number of students in 3 classes of a school is 333 . The number of students in class 1 and 2 are in 3:5 ratio and 2 and 3 class are 7:11 ratio . What is the strength of class that has highest number of students ?

Options

A. A) 125
B. B) 155
C. C) 135
D. D) 165

Answer

To solve the problem step by step, we will first define the number of students in each class based on the given ratios, then we will set up equations to find the number of students in each class.

### Step 1: Define the variables based on the ratios
Let the number of students in Class 1 be \(3x\) and in Class 2 be \(5x\) (since the ratio of Class 1 to Class 2 is 3:5).

Next, we know that the ratio of Class 2 to Class 3 is 7:11. Let the number of students in Class 3 be \(y\). Since Class 2 is also represented in the ratio with Class 3, we can express Class 2 in terms of \(y\):
\[ \frac{5x}{y} = \frac{7}{11} \implies 5x \cdot 11 = 7y \implies 55x = 7y \implies y = \frac{55x}{7} \]

### Step 2: Set up the total number of students
The total number of students in all three classes is given as 333. Therefore, we can write the equation:
\[ 3x + 5x + y = 333 \]
Substituting \(y\) from the previous step:
\[ 3x + 5x + \frac{55x}{7} = 333 \]
Combining like terms:
\[ 8x + \frac{55x}{7} = 333 \]
To eliminate the fraction, multiply the entire equation by 7:
\[ 7(8x) + 55x = 7 \cdot 333 \]
This simplifies to:
\[ 56x + 55x = 2331 \]
Combining the terms gives:
\[ 111x = 2331 \]

### Step 3: Solve for \(x\)
Now, divide both sides by 111:
\[ x = \frac{2331}{111} = 21 \]

### Step 4: Find the number of students in each class
Now that we have \(x\), we can find the number of students in each class:
- Class 1: \(3x = 3 \cdot 21 = 63\)
- Class 2: \(5x = 5 \cdot 21 = 105\)
- Class 3: \(y = \frac{55x}{7} = \frac{55 \cdot 21}{7} = 165\)

### Step 5: Determine which class has the highest number of students
Now we compare the number of students in each class:
- Class 1: 63
- Class 2: 105
- Class 3: 165

The class with the highest number of students is Class 3, which has 165 students.

### Final Answer
The strength of the class that has the highest number of students is **165**.

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