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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:

• find P percent from number A

 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.

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