Let's solve the questions from the image one by one.

b) i) Average Weight of Boys

• The average weight of 16 boys = 50.25 kg
• The average weight of 8 boys = 45.15 kg

To find the total weight of all the boys, we use the formula:

$\text{Total weight} = \text{Average weight} \times \text{Number of boys}$

• Total weight of 16 boys = $50.25 \times 16 = 804$ kg
• Total weight of 8 boys = $45.15 \times 8 = 361.2$ kg

Let the total weight of all boys be $W$, and there are $16 + 8 = 24$ boys. The total weight of the remaining 8 boys will be the difference between the total weight of 24 boys and the 8 boys already calculated.

The average weight of all boys is:

$\frac{804 + 361.2}{24} = \frac{1165.2}{24} = 48.55 \, \text{kg}$

So the answer is closest to C) 48.55 kg.

b) ii) Wrongly entered marks:

The average marks of the class increased by half because a wrong value of 83 was entered instead of 63. We can use the formula for the average:

$\text{New Average} = \frac{\text{Old Sum of marks} + 83}{n}$

$\text{Old Average} = \frac{\text{Old Sum of marks} + 63}{n}$

It’s given that the new average exceeds the old by $\frac{1}{2}$, leading to the equation:

$\frac{(S + 83)}{n} - \frac{(S + 63)}{n} = \frac{1}{2}$

Solving this will give us the number of pupils in the class.

I will continue with solving the remaining questions. Would you like to proceed with these first, or prefer explanations for a different part?