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{
  "topic": "percentage-of-percentage",
  "input_types": [
    "float",
    "float"
  ],
  "input_labels": [
    "X",
    "Y"
  ],
  "input_descriptions": [
    "Base Percentage",
    "Percentage on Base Percentage"
  ],
  "input_units": [
    "%",
    "%"
  ],
  "input_values": [
    "",
    ""
  ],
  "type": "Calculate",
  "title": "Percentage of Percentage",
  "category": "Percentage",
  "formula_mathjax": "\\( \\dfrac{ X \\cdot Y }{ 100 } \\)",
  "formula_mathjax_sub": "\\( \\dfrac{ X \\times Y }{ 100 } \\)",
  "formula": " ( X * Y ) / 100 ",
  "op_label": "X Percentage of Y Percentage",
  "output_unit": "%",
  "explanation": "Online Percentage of Percentage calculator enables you to find the percentage of a given percentage value. Enter the base percentage and the percentage of it in the input fields, and the answer is calculated.",
  "content": "<h2>Calculating Percentage of a Percentage</h2>\n<p>Calculating the percentage of a percentage is a common operation, particularly in situations where one percentage is applied to another. This is often seen in scenarios such as compounded discounts, multi-level commissions, or layered interest rates.</p>\n<p>The formula to calculate the percentage of a percentage is expressed as:</p>\n<p>\\( \\text{Result} = \\dfrac{ X \\times Y }{ 100 } \\)</p>\n<p>where:</p>\n<ul>\n<li><b>X</b> represents the base percentage.</li>\n<li><b>Y</b> represents the percentage applied to the base percentage.</li>\n</ul><p>By multiplying the two percentages and then dividing by 100, you obtain the percentage of the percentage.</p>\n\n<h2>Examples</h2><p>The following examples demonstrate how to calculate the percentage of a percentage using the given formula.</p><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> A real estate agent earns 5% commission on the sale price of a house. The agent’s broker takes 20% of the agent’s commission as a fee. What percentage of the house’s sale price does the broker take?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>X</b> = 5% (Agent’s commission percentage on the sale price)</li><li><b>Y</b> = 20% (Broker’s percentage of the agent’s commission)</li></ul><p>The formula to calculate the percentage of a percentage is:</p><p class=\"tabspace\">\\( \\text{Result} = \\dfrac{ X \\times Y }{ 100 } \\)</p><p>Substituting the given values into the formula:</p><p class=\"tabspace\">\\( \\text{Result} = \\dfrac{ 5 \\times 20 }{ 100 } \\)</p><p>Simplifying further:</p><p class=\"tabspace\">\\( \\text{Result} = 1\\% \\)</p><p class=\"tabspace answer\">Therefore, the broker takes 1% of the house’s sale price.</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> A company offers a 30% bonus to its employees based on their annual performance. Out of this bonus, 15% is allocated to the employee’s retirement fund. What percentage of the employee’s annual salary is added to the retirement fund?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li><b>X</b> = 30% (Bonus percentage)</li><li><b>Y</b> = 15% (Percentage of the bonus allocated to the retirement fund)</li></ul><p>The formula to calculate the percentage of a percentage is:</p><p class=\"tabspace\">\\( \\text{Result} = \\dfrac{ X \\times Y }{ 100 } \\)</p><p>Substituting the given values into the formula:</p><p class=\"tabspace\">\\( \\text{Result} = \\dfrac{ 30 \\times 15 }{ 100 } \\)</p><p>Simplifying further:</p><p class=\"tabspace\">\\( \\text{Result} = 4.5\\% \\)</p><p class=\"tabspace answer\">Therefore, 4.5% of the employee’s annual salary is added to the retirement fund.</p></div>"
}