# Find the number which is greater (less) than a given number by P percent.

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

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

B = A(1 + | P | ) |

100% |

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

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

B = A(1 - | P | ) |

100% |

**Derivation of formulas:**

A · P 100% -
add this number to A, if we need to find number B, which greater than A by P percent:

A + A · P = A(1 + P ) 100% 100% subtract this number from A, if we need to find number B, which less than A by P percent:

A - A · P = A(1 - P ) 100% 100%

## Examples of solving problems: find the number which is greater (less) than a given number by P percent

Example 1.

Find the number which is greater than 40 by 5%.
**Solution.**

40 · (1 + | 5% | ) = 42 |

100% |

**Answer:** the number 42 is greater than 40 by 5%.

Example 2.

Find the number which is less than 40 by 5%.
**Solution.**

40 · (1 - | 5% | ) = 38 |

100% |

**Answer:** the number 38 is less than 40 by 5%.

Example 3.

What amount will be a year in the bank if you put $ 1,000 on deposit at 10% per annum.
**Solution.**

1000 · (1 + | 10% | ) = 1100 |

100% |

**Answer:** on the deposit will be $ 1,100.

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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