This question requires simplifying a mathematical expression involving percentages.
Simplify Percentage Expression
The expression given is $(x\% \text{ of } y) + (y \% \text{ of } x)$. Let's break it down step-by-step:
Step 1: Convert Percentages to Fractions
Recall that $a\%$ is equivalent to $\frac{a}{100}$. Applying this:
- $x\% \text{ of } y = \frac{x}{100} \times y = \frac{xy}{100}$
- $y\% \text{ of } x = \frac{y}{100} \times x = \frac{yx}{100} = \frac{xy}{100}$
Step 2: Add the Terms
Now, add the results from Step 1:
$ \frac{xy}{100} + \frac{xy}{100} $
Step 3: Combine and Simplify
Adding the two fractions gives:
$ \frac{xy + xy}{100} = \frac{2xy}{100} $
Step 4: Express as a Percentage
The simplified term $\frac{2xy}{100}$ can be written back in percentage form. This is equivalent to $2\%$ of $xy$, because:
$ 2\% \text{ of } xy = \frac{2}{100} \times xy = \frac{2xy}{100} $
Thus, the original expression is equivalent to $2\%$ of $xy$.
Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
