ALGEBRA - solved problems
Basic percent formulas
29.    What is 25% of 80?
Solution: From the proportion,    
part : base (whole) = rate : 100    or    y : x = p : 100
then,   ,  and     
we calculate, the part or amount  y, the rate p and the base value x
Since given,  x = 80,   p% = 25%,   y = ?
Therefore,  
30.    What percent of 80 is 20?
Solution: Given,    y = 20,   x = 80,   p% = ?
Therefore,  
31.    What is the base value if  25% of it is 20?
Solution: Given,    p% = p/100 = 25%,   y = 20,   x = ?
Therefore,  
  The base value therefore   represents 1% of the base value.  
Percent increase or decrease,  base (x), amount (y), percent (p)
32.    In the price of $33 included is tax of 10%.  What is net price?
Solution: From the proportion,    
    x : 100 = ( x y ) : ( 100 p) then, y : p = ( x y ) : ( 100 p)  
 where   x   denotes original or base value x increased or decreased by amount y
then,  , and  
Since given,  x y = 33 ,   p% = 10%,   x = ?
Therefore,  
33.    Price reduced by 20% amounts to $320. How much is reduced?
Solution:    Given,  x -  y = 320 ,   p% = 20%,   y = ?
Therefore,  
Interest calculations
Simple interest
34.    Somebody deposits $20,000 into a savings account where the rate of interest is 4.8% annually.
How much money in interest will earn after nine months?
An amount of money deposited into a bank for a given period of time brings to the depositor a 
profit called interest
The amount of interest (I ) the bank pays you, depends on the interest rate ( i % ), the amount of money
deposited, denoted as principal P also called original balance (or initial investment), and the period of time n
the money is deposited,
since    P : 1 = I : (i n)    then,
Therefore, ,  and 
Solution:   Given,  P = $20000 ,   p% = 4.8%  and  n = 9 months,  I = ?
35.    A bank lends a company money for the six months period at a rate of  8% annually.
How much was lent if the company should pay $12,000 of interest?
Solution:   Given,  I = $12000 ,   p% = 8%  and  n = 6 months,  P = ?
36.    At what an interest rate was borrowed $75,000 for one year if $3,000 to interest is charged?
Solution:   Given,  P = $75000 ,   I = $3000  and  n = 1 year,  i = ?
37.    For what period of time should be deposited $200,000 at a 6% interest rate to earn $6,000
of interest?
Solution:   Given,  P = $200,000 ,  p% = 6%  and  I = $6,000,  n = ?
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