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# 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

All   -   100%
Part   -   100% + P

have proportion

 "All" = 100% => "All" = "Part" · 100% "Part" 100% + P 100% + P

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

All   -   100%
Part   -   100% - P

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%

Example 2.
Find the number if 63 less then this number by 10%.

Solution.

 63 · 100% = 70 100% - 10%

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.