On Sports Day, if 30 children were made to stand in a column, then 16 columns could be formed. If 24 children were made to stand in a column, then how many columns could be formed?

### Concept & Logic The total number of children participating remains constant regardless of how they are arranged. We can equate the total number of children in both scenarios to solve for the unknown. $$Total\ Children = Children\ per\ Column \times Number\ of\ Columns$$ ### Step-by-Step Solution * **Given:** * Scenario 1: 30 children/column creates 16 columns. * Scenario 2: 24 children/column creates an unknown number of columns ($C$). * **Calculation:** 1. Calculate the total number of children using the first scenario: $Total = 30 \times 16 = 480$ children. 2. Use this total to find the number of columns in the second scenario: $24 \times C = 480$ 3. Solve for $C$: $C = 480 / 24 = 20$ columns. ### Exam Strategy & Shortcut Use inverse proportionality. Equate the products directly without fully calculating the large total. $30 \times 16 = 24 \times C$ $C = \frac{30 \times 16}{24}$ Simplify by dividing 24 and 16 by 8: $C = \frac{30 \times 2}{3}$ $C = 10 \times 2 = 20$. ### Common Pitfall A common error is setting up a direct proportion instead of an inverse proportion (e.g., $30/16 = 24/x$), assuming fewer children per column means fewer columns. In reality, reducing the number of children per column requires *more* columns to hold the same total amount. ### Final Answer **Therefore, the correct answer is 20.**