
ALGEBRA
 solved problems







Basic percent formulas 


Solution: 
From the proportion, 

part
: base (whole) = rate : 100
or y
: x =
p
: 100 

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
±
y denotes original or base value x increased or decreased by amount
y 

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, 




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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