The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increases by 0.15 m. What is the average height of the 5 boys who leave ?

### Concept & Strategy When a subgroup leaves and the overall average *increases*, it means the departing subgroup had a lower average than the main group. They were pulling the average down. The total amount the average increased across the remaining members is equal to the "weight" the departing members left behind. $$Total\ Sum = Average \times Number\ of\ Entities$$ ### Step-by-Step Solution * **Calculate the initial total height:** For the 25 boys, the average is 1.4 m. $$Sum_{initial} = 25 \times 1.4 = 35\text{ m}$$ * **Calculate the new total height:** 5 boys leave, so 20 boys remain. The new average increases by 0.15 m, making it $1.4 + 0.15 = 1.55\text{ m}$. $$Sum_{new} = 20 \times 1.55 = 31\text{ m}$$ * **Find the total height of the 5 boys who left:** Subtract the new total from the initial total. $$Sum_{left} = 35 - 31 = 4\text{ m}$$ * **Calculate their average height:** Divide their total height by 5. $$Average_{left} = \frac{4}{5} = 0.8\text{ m}$$ ### Exam Strategy & Shortcut Use the **Deviation Method** to avoid multiplying large decimals. The 5 boys who left gave up $0.15\text{ m}$ to each of the remaining 20 boys. Total height they "gave away" to the group = $20 \times 0.15 = 3\text{ m}$. This means the 5 boys were 3 m *short* of maintaining the old average for their subgroup. If they had the old average, their sum would be $5 \times 1.4 = 7\text{ m}$. Since they were 3 m short, their actual sum is $7 - 3 = 4\text{ m}$. Average = $\frac{4}{5} = 0.8\text{ m}$. **One-line formula:** $$\text{Avg of Left} = \text{Old Avg} - \frac{\text{Remaining Members} \times \text{Increase in Avg}}{\text{Leaving Members}}$$ $$\text{Avg} = 1.4 - \frac{20 \times 0.15}{5} = 1.4 - 0.6 = 0.8\text{ m}$$ ### Common Pitfall Calculating the total increase ($20 \times 0.15 = 3$) and mistakenly subtracting it directly from the original average 1.4 m without distributing it across the 5 departing boys. The 3 m deficit belongs to all 5 boys collectively. ### Final Answer **Therefore, the correct answer is 0.8 m.**