Lesson OVERVIEW of lessons on percentage problems

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OVERVIEW of lessons on percentage problems


My lessons on percentage problems in this site are
    - Percentage problems
    - Percentage word problems (Type 1 problems, Finding the Part)
    - Percentage word problems (Type 2 problems, Finding the Rate)
    - Percentage word problems (Type 3 problems, Finding the Base)
    - Simple percentage problems
    - More complicated percentage problems
    - Advanced problems on percentage
    - Percentage problems on chains of discounts
    - Problems on percentage that lead to unexpected results
    - Simple interest percentage problems
    - Compounded interest percentage problems
    - Buying price, selling price and profit percentage problems
    - Business-related entertainment problem on percentage

List of lessons with short annotations

Percentage problems

Percentage word problems (Type 1 problems, Finding the Part)

        Problem 1. Test results.  The student answered  80  questions on the mathematics test.  95%  of answers were correct.  How many answers were correct?

        Problem 2. Tax calculation.  Calculator is advertised at  $24.99  plus  7.5%  tax at the store.  What is the total cost including tax?

        Problem 3. Discount.  Brian bought a printer on sale at the store.  The original price was  $90.00,  the discount was  15%.
                           What was the sale price of the printer?  How much money Brian saved?

        Problem 4. Population growth.  The population of Georgetown was  50000  in  2009.  The population had increased by  3  percents in  2010.
                           What was the population at the end of  2010?

        Problem 5. Investment.  Kathy invested  $25,000  to the bank account for  2%  per year.  What was the interest Kathy earned after one year?

        Problem 6. Alloy (mixture).  An alloy contains  70%  of silver.  How much silver is contained in  2.5  pounds of the alloy?


Percentage word problems (Type 2 problems, Finding the Rate)

        Problem 1. Test results.  The student answered  80  questions on the mathematics test.  76  of answers were correct.  What was the percent of correct answers?

        Problem 2. Tax calculation.  Daniel bought a calculator on-line.  The calculator was advertised at  $24.99  before the tax.  When the tax was included,
                           Daniel paid  $26.86.  What percent of his money did he spend on tax?

        Problem 3. Discount.  Brian bought a printer on sale at a store.  The original price was  $90.00.  After a discount was applied,  Brian paid  $76.50  only.
                           What percent the discount was?

        Problem 4. Population growth.  The population of Georgetown was  50000  at the end of  2009.  The population had increased to  51500  at the end of  2010.
                           What percent of increase is this?

        Problem 5. Investment.  Kathy invested  $25,000  into the bank account.  One year later her account had increased to  $25,500.  What was the annual interest rate?

        Problem 6. Alloy (mixture).  An alloy weights  2.5  pounds.  It contains  1.75  pounds of silver.  What is the percent of silver in the alloy?


Percentage word problems (Type 3 problems, Finding the Base)

        Problem 1. Test results.  The student answered correctly  76  questions on the mathematics test,  which was  95%  of the total number of questions.
                           How many questions were there in the test?

        Problem 2. Tax calculation.  Daniel bought a calculator at the store with the tax of  7.5%.  The tax amount was  $1.87.  Find the calculator price before tax.

        Problem 3. Discount.  Brian bought a printer on sale at the store.  The discount was  15%,  and Brian saved  $13.50.  What was the printer original price?

        Problem 4. Population growth.  The population of Georgetown was  50000  in  2009.  The population increased by  3  percents in  2010,  or  1500.
                           What was the population at the end of  2009?

        Problem 5. Investment.  Kathy invested into the bank account for  2%  per year.  After one year,  Kathy earned  $500.00  in this account.
                           What was Kathy's initial investment?

        Problem 6. Alloy (mixture).  An alloy contains  70%  of silver.  The amount of silver in the alloy is  1.75  pounds.  Find the weight of the alloy.


Simple percentage problems

        Problem 1.  Harold  is a salesperson in a retail store and earns  $48  per week plus  12%  of his weekly sales.
                           If Harold made  $600  one week,  what were his sales that week?

        Problem 2.  IBM  states that it makes a  30%  profit over its expenses for producing hard drives.
                           IBM  sells each hard drive for  $390.  How much does it cost  IBM  to make each hard drive?

        Problem 3.  Find last year salary,  if after a  3%  raise this year salary is  $3080.

        Problem 4.  A new television set was recently purchased for  $486  including tax.
                           If the tax rate is  8% ,  find the price of the television set before taxes.

        Problem 5.  A bakery owner sold her last two cakes for  $36  each.  She made a profit of  25%  on one cake,
                           but had an  10%  loss on the other.  What was the total profit or loss on the two sales?

        Problem 6.  Ngesu was allowed a discount of  11%  for goods worth sh. 8,000 and a discount of  8.6 % for goods worth sh. 17,000.
                           What percentage discount was she allowed altogether ?


More complicated percentage problems

        Problem 1.  Car  A  has wheels with the diameter in  10%  more than the car  B  has.
                           But the wheels of the car  A  rotate in  10%  slower than the wheels of the car  B.  Which of the two cars moves faster?

        Problem 2.  Car  A  has wheels with the diameter in  10%  more than the car  B  has.
                           But the wheels of the car  B  rotate in  10%  faster than the wheels of the car  A.  Compare the speed of the two cars.

        Problem 3.  The rod  B  is in  10%  longer than the rod  A.  The rod  C  is in  10%  shorter than the rod  B.
                           Compare the lengths of the rods  A  and  C.

        Problem 4.  Two students Bert and Sol left the same house at the same time.  They both walk to school.
                           Each step of Bert is  20% shorter than each step of Sol,  however,  the number of steps Bert takes is  20% more then the number of steps
                           Sol takes in the same amount of time.  Who will get to the school faster?

        Problem 5.  A salesman sold  2  refrigerators for  $1200  each.  The first sold at  20%  profit and the second was sold at  20%  loss.
                           Find the salesman's net profit or loss.


Advanced problems on percentage

        Problem 1.  In a basket full of balls,  60%  are mangoes and remaining  40%  are apple.  25%  of apples are green and the rest  75%  are red.
                           Of the mangoes,  80%  are red and the rest of the mangoes are green.  What percentage of the green fruits are mangoes?

        Problem 2.  The mass of a bag of red star sugar is  20%  greater than the mass of a bag of blue star sugar.
                           However,  a bag of red star sugar costs  50%  more than a bag of blue star sugar.
                           For the same mass,  red star sugar costs how much percent more than blue star sugar?

        Problem 3.  Before the rise in  VAT  from  17.5%  to  20%  the price of a table was  $499.
                           To the nearest  $1,  what is the price of the table after the increase in  VAT ?

        Problem 4.  Sandra saves  15%  of her salary for retirement.  This year her salary was  $1,000  more than in the previous year,
                           and she saved  $7,350.  What was her salary in the previous year?

        Problem 5.  A farmer sells sheep at  $75  a head.  The sheep cost  $x  each.  The farmer finds she has made  x%  profit on the sale of the sheep.  Find  x.

        Problem 6.  Suppose you accumulated  $500,000,  perhaps from many years of saving.  You put the money in a savings plan
                           earning  6%  compounded monthly.  If you want to live off the interest without disturbing the  $500,000  balance,
                           what amount can you withdraw at the beginning of each month?

        Problem 7.  Two certificates of deposit pay interest at rates that differ by  4%.  Money invested for one year in the first  CD  earns  $350 interest.
                           The same principal invested in the other  CD  earns  $550.  Find the two rates of interest.


Percentage problems on chains of discounts

        Problem 1.  A store reduces the price of a  CD  player by  20%  and then reduces that price by  15%.
                           If the final price of the  CD  player is  $170,  what was its original price?

        Problem 2.  A  TV  that usually sells for  $195.72  is on sale for  20%  off.
                           If sales tax on the  TV  is  9%,  what is the price of the  TV,  including tax?

        Problem 3.  CHMCO  sells a product with discounts of  25%,  15%  to its distributors.  It plans to allow a seasonal discount
                           to make the overall discount equal to  45%.  What additional  (chained)  discount should  CHMCO  allow?

        Problem 4.  A certain type of piano costs the dealer  $6,490.  If the dealer wants to offer customers a discount of  15%  off
                           the price marked and still make a profit of  15%,  what must be the marked price of the piano to the nearest dollar?

        Problem 5.  The price of a stock appreciated by  20%  of its value last month
                           and then depreciated by  20%  this month. By what percent did the stock
                           appreciate or depreciate over the  2-month period?

        Problem 6.  A stock price is currently at  $10.  What will be the probability the stock price will be above  $10  after  5  days?
                           Assume the stock price will be randomly moved according to the following exact percentages:  -3%,  -2%,  -1%,  1%,  2%  and  3%
                           (so there are total  6  different possible percentages values of increase/decrease without repeating and the percentage values
                           are purely random for each day under the above condition).


Problems on percentage that lead to unexpected results

        Problem 1.  Water makes up  96%  of the mass of an apricot.  When apricots were left out in the sun,  some water evaporated,  and water then
                           makes up  95%  of the mass of the sun dried apricots.  What percentage of its original mass do the apricots lose when the water evaporates?

        Problem 2.  A raisin is a dried grape.  Originally,  grapes contain  98%  of water by mass.
                           100 kilograms of grapes were dried and water content was decreased till  96%.  Find the mass of the raisins obtained.


Simple interest percentage problems

        Problem 1.  Jane invests  $2,000  in a saving account.  The account pays an annual simple interest rate
                           of  5.75%  at the end of each year.  How much will be in her account at the end of  10  years?

        Problem 2.  Nate borrows  $300  to buy a smartphone.  He is charged  5%  simple interest per year.
                           How much interest,  in dollars,  will Nate pay after  2  years?

        Problem 3.  Money is borrowed at  11​%  simple interest.  After one​ year,  ​$1292.04 pays off the loan.
                           How much was originally​ borrowed?


Compounded interest percentage problems

        Problem 1.  Stan has a  $18,200  certificate of deposit that earns  4.8%  interest compounded quarterly for  5  years.
                           What is the compound interest after  5  years?

        Problem 2.  When Sophie was born her parents invested a sum of  $20,000  in her college fund.  They invested it
                           at a nominal annual rate of  5%  with interest compounded quarterly.  Find the value at the account
                           in the account after 18 years assuming that no other deposits or withdrawals are made.

        Problem 3.  Omar will need  $25,000  in  12  years for new machinery for his shop.
                           How much should he invest now at  4.5%  annual interest,  compounded monthly,  to reach his goal?

        Problem 4.  How much must be deposited today into account with annual compounding and an APR of  5​%
                           in order to have  $25000  in  7  years?

        Problem 5.  Mr.Popo deposited on a savings bank earning  5%  per year compounded annually.  After  3  years,
                           he decided to transfer the accumulated amount to an investment bank which earns  8%  per year compounded quarterly.
                           If the accumulated amount after six years in the investment bank is  102,408.19,  how much did he deposit on the savings bank?

        Problem 6.  Which account has the highest annual interest rate?
                             A.   Account 1:  Interest is compounded daily at a rate of  5.25%.
                             B.   Account 2:  Interest is compounded monthly at a rate of  5.40%.
                             C.   Account 3:  Interest is compounded quarterly at a rate of  5.50%.
                             D.   Account 4:  Interest is compounded annually at a rate of  5.55%.


Buying price, selling price and profit percentage problems

        Problem 1.  The marked price of a pillow is  $240.  The shop makes a profit of  28%  by selling
                           the pillow at a discount of  20%.  Find the cost price of the pillow.

        Problem 2.  An article is sold at a discount of  10%  and a profit of  20%  is made.
                           If the cost price of the article is  $3600,  find its marked price.

        Problem 3.  AXY  men’s sportswear is planning to sell its new line of pants to retail outlets.
                           The cost to the retailer will be  $33  per pair of pants.  As a convenience to the retailer,
                           AXY  will attach a price tag to each pair.  What amount should be marked on the price tag so
                           that the retailer may reduce this price by  20%  during a sale and still make a profit of  15%  on the cost?


Business-related entertainment problem on percentage

        Problem 1.  A man borrowed from a bank under a promissory note that he signed in the amount of  $25,000
                           for a period of one year.  He received only the amount of  $21,915  after the bank collected
                           the advance interest and additional amount of  $85  for notarial and inspection fees.
                           What was the rate of interest that the bank collected in advance?

        Problem 2.  Grace sells two sets of commemorative coins for  $750 each.  She gains  25%  on one and lose  25%  on the other.
                           Find the overall profit or loss percent.


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