# Find the number A if known number B which greater (less) than A by P percent.

## Formula for calculating the number A if known number B which is greater than A by P percent.

If we have the number B, which is greater then A by P percent and need to find A, then

A = | B · 100% |

100% + P |

## Formula for calculating the number A if known number B which is less than A by P percent.

If we have the number B, which is less then A by P percent and need to find A, then

A = | B · 100% |

100% - P |

For the derivation of this equation using the method of solving problems with percentage

If "Part" more then "All" by P percent then

have proportion

"All" | = | 100% | => | "All" = | "Part" · 100% |

"Part" | 100% + P | 100% + P |

If "Part" less then "All" by P percent then

have proportion

"All" | = | 100% | => | "All" = | "Part" · 100% |

"Part" | 100% - P | 100% - P |

## Examples of calculating number A if known number B which greater (less) than A by P percent.

Example 1.

Find the number if 66 greater then this number by 10%.
**Solution.**

66 · 100% | = 60 |

100% + 10% |

**Answer:** 60.

Example 2.

Find the number if 63 less then this number by 10%.
**Solution.**

63 · 100% | = 70 |

100% - 10% |

**Answer:** 70.

Example 3.

Client put money on deposit in the bank at 12% per annum, a year later the he have $ 33,600. How much money client put on the deposit?
**Solution.**

33,600 · 100% | = 30,000 |

100% + 12% |

**Answer:** client put on the deposit $ 30,000.

Percent
Percent Definition. Main information
Decimal to Percent. Percent to Decimal
The method of solving problems with percentage

The most common types of problems with percent:
Find P percent of A
B is P percent of what?
B is what percent of A?
Find the number which is greater (less) than a given number by P percent
Find the number A if known number B which greater (less) than A by P percent

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