Let's break down the problem and solve it step by step:

Given Data:

• The average score of boys in the examination = 71
• The average score of girls in the examination = 73
• The overall average score of the school = 71.8

Let:

• $B$ = number of boys
• $G$ = number of girls

Formula for Average:

The overall average score of the school can be written as a weighted average of the scores of boys and girls:

$\text{Overall Average} = \frac{(B \times \text{Average score of boys}) + (G \times \text{Average score of girls})}{B + G}$

Substitute the given values:

$71.8 = \frac{(B \times 71) + (G \times 73)}{B + G}$

Now, multiply both sides by $B + G$ to eliminate the denominator:

$71.8 \times (B + G) = (B \times 71) + (G \times 73)$

Expand both sides:

$71.8B + 71.8G = 71B + 73G$

Now, move all the terms involving $B$ to one side and the terms involving $G$ to the other side:

$71.8B - 71B = 73G - 71.8G$

This simplifies to:

$0.8B = 1.2G$

Now, solve for the ratio of $B$ to $G$:

$\frac{B}{G} = \frac{1.2}{0.8} = \frac{3}{2}$

Final Answer:

The ratio of the number of boys to the number of girls is 3:2.

Would you like more details or have any further questions on this?

Related Questions:

1. What would happen to the ratio if the overall average were 72.5?
2. How would you calculate the total number of boys and girls if the total students were 60?
3. How does a weighted average differ from a simple average?
4. If the average score of the boys were 75, how would that affect the ratio?
5. Can you explain how ratios can be applied in other real-life scenarios?

Tip:

In weighted averages, it's important to consider both the values and the quantities to get an accurate overall average.