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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.

In the study of percent to you also will be helpful:

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