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 B?

Options

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

Answer

To solve the problem step by step, we will break down the information provided and use it to find the average marks of students in class B.

### Step 1: Define Variables
Let the number of students in class B be \( x \). Then, the number of students in class A, which is 40% more than that in B, can be expressed 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:
\[ 1.4x + x = 72 \]
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, and the number of students in class A is:
\[ 1.4x = 1.4 \times 30 = 42 \]

### Step 4: Define Average Marks
Let the average marks of students in class A be \( a \). The average marks of students in class B, which is 50% more than that of A, can be expressed as:
\[ \text{Average marks of B} = a + 0.5a = 1.5a \]

### Step 5: Set Up the Average Marks Equation
The average marks of all students in classes A and B is given as 58. Therefore, we can set up the equation for the total marks:
\[ \frac{(42 \times a) + (30 \times 1.5a)}{72} = 58 \]
This simplifies to:
\[ \frac{42a + 45a}{72} = 58 \]
Combining the terms gives:
\[ \frac{87a}{72} = 58 \]

### Step 6: Solve for \( a \)
To solve for \( a \), multiply both sides by 72:
\[ 87a = 58 \times 72 \]
Calculating the right side:
\[ 87a = 4176 \]
Now, divide both sides by 87:
\[ a = \frac{4176}{87} = 48 \]

### Step 7: Find Average Marks of B
Now that we have \( a \), we can find the average marks of students in class B:
\[ \text{Average marks of B} = 1.5a = 1.5 \times 48 = 72 \]

### Final Answer
The average marks of students in class B is **72**.

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