Two sections of class `10^(th)` A and B have 30 and 35 students respectively. Average score of Maths of section A is 70 and average score of section A and B is 62. Find the average score of section B.

Answer

To find the average score of section B, we can follow these steps:

### Step 1: Understand the problem
We have two sections, A and B, with the following information:
- Section A has 30 students with an average score of 70.
- Section B has 35 students, and we need to find its average score.
- The combined average score of both sections is 62.

### Step 2: Set up the equation for combined average
The formula for the combined average of two groups is given by:

\[ \text{Combined Average} = \frac{(N_1 \times A_1) + (N_2 \times A_2)}{N_1 + N_2} \]

Where:
- \(N_1\) = number of students in section A = 30
- \(A_1\) = average score of section A = 70
- \(N_2\) = number of students in section B = 35
- \(A_2\) = average score of section B (unknown)

Substituting the known values into the formula gives us:

\[ 62 = \frac{(30 \times 70) + (35 \times A_2)}{30 + 35} \]

### Step 3: Simplify the equation
Calculate \(30 + 35\):

\[ 30 + 35 = 65 \]

Now, substituting this back into the equation:

\[ 62 = \frac{2100 + 35A_2}{65} \]

### Step 4: Eliminate the denominator
Multiply both sides by 65 to eliminate the fraction:

\[ 62 \times 65 = 2100 + 35A_2 \]

Calculating \(62 \times 65\):

\[ 62 \times 65 = 4030 \]

So, we have:

\[ 4030 = 2100 + 35A_2 \]

### Step 5: Solve for \(A_2\)
Subtract 2100 from both sides:

\[ 4030 - 2100 = 35A_2 \]

Calculating the left side:

\[ 1930 = 35A_2 \]

Now, divide both sides by 35 to find \(A_2\):

\[ A_2 = \frac{1930}{35} \]

### Step 6: Perform the division
Now, we can simplify \( \frac{1930}{35} \):

Dividing 1930 by 5 gives:

\[ \frac{1930 \div 5}{35 \div 5} = \frac{386}{7} \]

### Step 7: Calculate the average score of section B
Now, we perform the division \(386 \div 7\):

Calculating gives:

\[ 386 \div 7 = 55 \text{ remainder } 1 \]

So, we can express this as:

\[ 55 \frac{1}{7} \]

Thus, the average score of section B is:

\[ A_2 = 55 \frac{1}{7} \]

### Final Answer
The average score of section B is \(55 \frac{1}{7}\).

---