The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20 kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

### Concept & Strategy This problem is best solved using the Rule of Alligation. Alligation allows us to quickly find the ratio in which two groups (with specific averages) must be mixed to produce a combined group with a known overall average. $$\frac{\text{Quantity of Group 1}}{\text{Quantity of Group 2}} = \frac{\text{Average of Group 2} - \text{Overall Average}}{\text{Overall Average} - \text{Average of Group 1}}$$ (Taking absolute differences) ### Step-by-Step Solution * **Given Data:** Average of Boys = 30 kg Average of Girls = 20 kg Combined Average = 23.25 kg * **Applying Alligation:** Let's set up the alligation cross: Boys (30) --------- Girls (20) \ / Mix (23.25) / \ (23.25 - 20) (30 - 23.25) * **Calculating the Ratio:** Ratio of Boys to Girls = $(23.25 - 20) : (30 - 23.25)$ Ratio = $3.25 : 6.75$ * **Simplifying the Ratio:** Multiply both sides by 100 to remove decimals: $325 : 675$ Divide both sides by 25: $13 : 27$ * **Conclusion:** The ratio of boys to girls in the class must be $13 : 27$. Looking at the given options, option (b) provides exactly 13 boys and 27 girls, which satisfies this ratio. ### Exam Strategy & Shortcut Whenever a question asks for a ratio or "possible strength" based on two distinct sub-group averages combining into a total average, **never** use standard $x$ and $y$ algebra equations in an exam. Alligation is visually intuitive and instantly gives you the ratio $(23.25 - 20)$ to $(30 - 23.25) \rightarrow 3.25 : 6.75 \rightarrow 13 : 27$. You can scan the options to see which one fits this exact ratio. ### Common Pitfall A common mistake is applying the alligation subtraction backwards and getting the ratio flipped as $27 : 13$. Always ensure you map the difference on the diagonals correctly: the quantity of Boys corresponds to the difference between Girls' average and the Mix average. ### Final Answer **Therefore, the correct answer is 13 and 27.**