Ten percent of twenty plus twenty percent of ten equals

### Concept & Formula This question tests the commutative property of percentages. The fundamental rule of percentages is that $x\%$ of $y$ is always equal to $y\%$ of $x$. This principle makes seemingly complex summations much easier to resolve mentally. $$ x\% \times y = y\% \times x $$ ### Step-by-Step Solution **Given:** * First term: $10\%$ of $20$ * Second term: $20\%$ of $10$ **Calculation / Deduction:** * Calculate the first term: $10\%$ of $20 = \frac{10}{100} \times 20 = 2$ * Calculate the second term: $20\%$ of $10 = \frac{20}{100} \times 10 = 2$ * Add the two results together: $2 + 2 = 4$ * Now, evaluate the given options to find which one equals $4$: (a) $10\%$ of $20 = 2$ (b) $20\%$ of $10 = 2$ (c) $1\%$ of $200 = 2$ (d) $2\%$ of $200 = \frac{2}{100} \times 200 = 4$ * Option (d) is the only expression that evaluates to the sum of $4$. ### Exam Strategy & Shortcut Using the rule $A\%$ of $B = B\%$ of $A$, you can immediately see that "$10\%$ of $20$" is the exact same value as "$20\%$ of $10$". Therefore, you are simply calculating $2 \times (10\%$ of $20)$. Since $10\%$ of $20$ is $2$, the total is obviously $4$. Scanning the options, $2\%$ of $200$ clearly yields $4$. This requires zero paper calculation. ### Common Pitfall Students often skim the options and hastily select (a) or (b), mistaking one part of the question for the total sum. Always remember to complete the addition operation before checking the options. ### Final Answer Therefore, the correct answer is **2 percent of 200**.