**Result = (P1 / 100) × (P2 / 100) × V, the percentage of a percentage calculator is a designed to determine the result when one percentage is applied to another percentage. **

## Percentage of a Percentage Calculator

First Percentage | Second Percentage | Calculation Process | Final Result |
---|---|---|---|

50% | 40% | (50 × 40) ÷ 100 | 20% |

75% | 60% | (75 × 60) ÷ 100 | 45% |

25% | 80% | (25 × 80) ÷ 100 | 20% |

90% | 30% | (90 × 30) ÷ 100 | 27% |

45% | 70% | (45 × 70) ÷ 100 | 31.5% |

10% | 50% | (10 × 50) ÷ 100 | 5% |

85% | 20% | (85 × 20) ÷ 100 | 17% |

60% | 90% | (60 × 90) ÷ 100 | 54% |

30% | 25% | (30 × 25) ÷ 100 | 7.5% |

15% | 10% | (15 × 10) ÷ 100 | 1.5% |

55% | 45% | (55 × 45) ÷ 100 | 24.75% |

22% | 33% | (22 × 33) ÷ 100 | 7.26% |

95% | 15% | (95 × 15) ÷ 100 | 14.25% |

40% | 75% | (40 × 75) ÷ 100 | 30% |

70% | 50% | (70 × 50) ÷ 100 | 35% |

## Percentage of a Percentage Formula

The **formula** for calculating a percentage of a percentage is:

`Result = (P1 / 100) × (P2 / 100) × V`

To express this mathematically:

**If P1 = First Percentage
P2 = Second Percentage
Then, Final Percentage = (P1 × P2) ÷ 100**

To find **40% of 25%**:

**(40 × 25) ÷ 100 = 1000 ÷ 100 = 10%**

## How to Find a Percent of a Percent?

**Calculate the First Percentage**: V1 = (P1 / 100) × V**Calculate the Second Percentage of the First Result**: V2 = (P2 / 100) × V1**Combining Both Calculations**: To find the final result V2 directly from the original value V: V2 = (P1 / 100) × (P2 / 100) × V

**Assume we want to calculate 20% of 50% of 200.**

**Calculate 50% of 200**: Let P2 = 50, V = 200: V1 = (50 / 100) × 200 = 100

**Calculate 20% of 100**: Let P1 = 20: V2 = (20 / 100) × 100 = 20

The final result is: **V2 = 20**

To find **65% of 80%**:

- Convert to decimals:

- 65% = 0.65
- 80% = 0.80
- Multiply: 0.65 × 0.80 = 0.52
- Convert back to percentage: 0.52 × 100 =
52%

A clothing store offers a **40% discount** on all items. During a special sale, they offer an additional **25% off** the already discounted price.

- Original price: $100
- First discount:
40% off= $60 remaining- Second discount:
25% of 60%(remaining percentage)- Calculation: (25 × 60) ÷ 100 =
15%- Final price: $100 × (1 – 0.55) = $45

### References:

- Purplemath – Working with Percentages https://www.purplemath.com/modules/percents.htm
- Mathematics Stack Exchange https://math.stackexchange.com/questions/tagged/percentages

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