The total number of students in class A and B is 72. The number of students in A is 40% more than that in B. The average marks of students in B are 50% more than that of students in A. If the average marks of all the students in A and B are 58, then what are the average marks of students in A ?

Options

A. 58
B. 72
C. 50
D. 48

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the number of students in class B be \( x \). Since the number of students in class A is 40% more than in class B, we can express the number of students in class A as:
\[ \text{Number of students in A} = x + 0.4x = 1.4x \]

### Step 2: Set Up the Total Students Equation
According to the problem, the total number of students in classes A and B is 72:
\[ x + 1.4x = 72 \]
Combining the terms gives:
\[ 2.4x = 72 \]

### Step 3: Solve for \( x \)
To find \( x \), divide both sides by 2.4:
\[ x = \frac{72}{2.4} = 30 \]
Thus, the number of students in class B is \( 30 \).

### Step 4: Calculate the Number of Students in Class A
Using the value of \( x \):
\[ \text{Number of students in A} = 1.4x = 1.4 \times 30 = 42 \]

### Step 5: Define Average Marks Variables
Let the average marks of students in class A be \( 2x \) and the average marks of students in class B be \( 3x \). According to the problem, the average marks of students in B are 50% more than those in A:
\[ \text{Average marks in B} = 2x + 0.5(2x) = 3x \]

### Step 6: Set Up the Average Marks Equation
The average marks of all students in A and B is given as 58:
\[ \frac{(42 \times 2x) + (30 \times 3x)}{72} = 58 \]

### Step 7: Simplify the Equation
Multiply both sides by 72:
\[ (42 \times 2x) + (30 \times 3x) = 58 \times 72 \]
Calculating \( 58 \times 72 \):
\[ 58 \times 72 = 4176 \]
So, we have:
\[ 84x + 90x = 4176 \]
Combining the terms gives:
\[ 174x = 4176 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 174:
\[ x = \frac{4176}{174} = 24 \]

### Step 9: Find the Average Marks of Students in Class A
Since we defined the average marks of students in class A as \( 2x \):
\[ \text{Average marks in A} = 2 \times 24 = 48 \]

### Final Answer
The average marks of students in class A is **48**.

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